I know I'm basically just reiterating the earlier answers here, as most of these points have already been raised in one form or another (by F'x and scaaahu in particular), but I'd just like to add my summary of how I'd approach the problem.
[Note: Oh, wow, this answer turned out way longer than I thought it would. If you don't want to read all of it, I've highlighted the key parts so you can just skip the rest.]
For some background, I'm a graduate student in Helsinki, and I've grown up and studied in Finland. While Finns generally aren't quite as focused on "face" as people from some Asian cultures are said to be, we do tend to be rather shy and quiet, and sayings like "talk is silver, silence is gold" or "it is better to keep your mouth shut and appear stupid than to open it and remove all doubt" definitely find resonance here. Thus, getting a lively classroom discussion going here can indeed be hard, something which I've heard several teachers from other parts of the world comment on.
First, as you correctly note, you will need to make the students understand the importance of the assignments, and vague threats of "I may have to fail you" aren't going to do it. It's completely natural for students to try to minimize their workload, and if they think they can pass the course without doing the homework, most of them (except the few truly motivated ones) won't do it. And if enough of them think so, it's likely to become a self-fulfilling prophecy, unless you're actually willing to fail the majority of your class.
To address that, I'd suggest that you introduce a points system and make it clear to the students that:
- X points total are required to pass the course,
- each exam / project (out of m during the course) is worth up to Y points,
- each discussion class (out of n) is worth an additional Z points, and
- getting any points for a discussion class requires active participation in the discussion.
Having all this clearly set out in advance lets the students make their own informed decisions about how to prioritize their tasks. In particular, setting a definite pass/fail threshold means that they'll know exactly how much work they need to do to pass the course, and that if they don't meet that threshold, they will fail.
Yes, some students will probably use this as an excuse to skip some fraction of the discussion classes, figuring that they'll still score enough points in the exams to pass — but those are the same students who otherwise probably wouldn't bother with the homework at all, figuring that you wouldn't fail them just for that as long as they did reasonably well in the exams.
Choosing the point scores and thresholds is up to you, but a fairly common choice around here seems to be that the exams make up 50% of the possible points, and 50% of the total is also the minimum level needed to pass. Thus, in principle, one can pass the course without any classroom participation... as long as one is confident of getting an absolutely perfect exam score. (FWIW, as a personal anecdote, I did that once as an undergrad — I signed up for the final exam of a course with such a grading policy, mistakenly thinking it was a stand-alone exam, and managed to just barely pass. Got the lowest possible passing grade, though.)
So much for the stick; you'll also want a carrot to go with it. I'd suggest telling your students that the aim of the course is not to stress them out, and that you're willing to adjust the homework to fit their workload, within reason, as long as they'll tell you in advance when they expect to be busy and when they'll have more time. Depending on how varied your students' schedules are, this might even involve some personalized assignments for students who, for some reason, won't be able to attend as many classes as they want or need to.
Such small kindnesses go a long way towards building goodwill and motivation, but there's a more subtle trick involved here as well: asking for adjustments to the homework is itself a form of classroom participation. Sure, it doesn't actually involve the subject of the course in any direct way, but as scaaahu notes, an important part of the process is to just get the students to speak up in class about something, whatever it is.
Another reason why discussing the appropriate amount of homework with the students can help is that, psychologically, being involved in making a rule makes people feel invested in it, and thus much more likely to follow it than if it were simply imposed on them by an external authority. I'm pretty sure there's actual psychological research on this, if I just knew the right keywords to find it, but it's definitely an effect I've noticed in practice. Effectively, by setting up a mutual agreement with your students about the appropriate level of homework, you're depriving them of the mental excuse that "there's way too much stuff for me to do, I'll never have time for this."
As I already wrote above, I also think scaaahu's suggestion of encouraging classroom discussion in any form, just to get the students used to it, is a good idea. In particular, while stressing that active participation is necessary to earn points for a discussion class, I'd also suggest explicitly noting that having read or understood the material is not required (albeit highly recommended), as long as one is willing to ask questions and discuss the topic. Of course, you can still make demonstrated familiarity with the material a requirement for getting the full points, if you want.
One way in which that could help is that, just possibly, some of the students who say they haven't read the material (but can't say why not) actually have read it, but just don't feel that they've understood it well enough to discuss it without "appearing stupid" or "losing face". If you manage to convince those students that they'll at least have to ask questions about the material, they may even come to realize that their understanding of it is neither as poor nor as embarrassing as they thought.
Finally, since I mentioned my background in the beginning, let me include a couple of tips and traps I've noticed specifically regarding Finnish audiences. I can't say whether or not these might apply also to your students, but they may be at least worth considering. (There are also some implicit assumptions about classroom style in the way I've presented things below, but the general points should be adaptable to different teaching methodologies.)
(Also, just to be clear, by "Finns" here I really mean "me, and some other people I've observed in class". Of course, as with any cultural or ethnic group, there's a huge amount of within-group variation, so nothing here should be construed as universal rules.)
One is that Finns generally don't like to interrupt when someone else is talking; it's considered rude. By the same token, if they do feel the need to interrupt you, they're likely to just politely clear their throat (or, in a classroom setting, raise their hand) or say "excuse me..." and wait for you to stop. Thus, one way to kill off any hope of an active classroom discussion is to just talk too much yourself.
Going off on a long uninterruptible monologue whenever someone asks something remotely relevant is particularly bad — you may think you're rewarding the asker by seizing on the topic they brought up, but it's more likely that you're just teaching everyone in the class not to ask too many questions if they want to get on with the course. Engaging the asker in a back-and-forth discussion is a much better approach, both because it gives them a better chance to participate, but also just because it gives them a chance to tell you "oh, I get it now, thanks!" without having to interrupt you.
Another trap is that Finnish students tend to be quite reluctant to answer questions which they consider trivial — there are several reasons for that, but I suspect it's partly a side effect of the early school system, where the teachers generally try to learn the progress level of each child and to direct questions of different levels to different students. While this is generally an excellent way of dealing with a heterogeneous group of students and making sure everyone gets to participate, it does have the side effect of teaching the more advanced students (who, of course, are the ones who mostly end up in academia later) not to even bother raising their hand for questions they feel are below their level, since they won't get to answer them anyway.
The problem here is that, if you don't already know your students well, you can end up asking a question and getting no answers, and having no idea whether the question was way too easy or way too hard (or just possibly both). My suggestion for dealing with that situation would be to ask something like "OK, so you all know this?" and seeing who nods. If not all do, direct the question to someone who didn't.
A third point, somewhat related to the first, is that Finns stereotypically don't like asking questions if they believe they can find the answer by just listening or reading more instead. (If you look at my Stack Exchange profile, you'll see that I'm a perfect example of the stereotype; I just counted that, excluding meta sites and code golf, I've posted well over a thousand answers and just four questions across the entire network. And most of those are self-answered.) If your students are like that too, they may be much more likely to speak up if they believe they have a reason to disagree with you than if they just don't understand something (even if they might actually phrase their argument as a question).
One rather cheap, but potentially effective, trick to encourage student participation in situations like that could be to deliberately make trivial mistakes, like replacing a plus sign with a minus in a simple equation, and see if your students spot them. If they do, thank them and encourage them to keep an eye out for anything else that might seem funny. If they don't, you can always just "notice" the mistake yourself a little later and correct it. Either way, you end up looking a little less like an infallible authority.
And, yeah, I realize that I've gone way off on a tangent at this point, so I'll just stop here. Sorry.