US universities typically organize visit weekends for newly admitted graduates, after which the latter confirm or refuse the offer. Is there any research/study/survey that looked at the impact of the visit weekend weather on the admitted graduates' grad school decision?
The short non-scientific answer: YES
My answer is just based on anecdotes and I am not aware of any methodological research on this subject (it is not my field of research). I've listened to an episode of This American Life about this subject, in which they interview professors on the admission committees of different universities. According the the interviews, visiting a university is a good indication that the student is interested in the school and is more likely to attend the school if he/she is admitted.
This is episode "504: How I Got Into College" of the podcast, which you can find here (http://www.thisamericanlife.org/radio-archives/episode/504/how-i-got-into-college).
P.S. I tried to post this as a comment to the question but it was too long. I apologize if this is not the answer you are looking for.
I'm not aware of any research, and we've actually debated this some in my department.
Anecdotally, the biggest factor in whether a prospective grad student decides to attend is whether they come to visit. Of course, that's hard to establish as causal, since students who are inclined to turn down the offer are much less likely to visit. Moreover, we know of a few students each year who already accepted our offers who come for the visit weekend(s).
I suspect weather is pretty low on the list of reasons to decline a program.
We've polled students who declined our offer and generally the reason is either that they preferred an advisor at another school, or preferred a higher-ranked program. I don't have the spreadsheet, but I think that was ~75-80% of the respondents over the last two years of polling. (In our chemistry department, the incoming grad student class is ~30-40, so the statistics are reasonable.)
I do agree with the comment above about significantly negative experiences. We sometimes took students to eat at a cool restaurant that used to be a church. One student, who was evidently, extremely Catholic, was offended, even though we explained the church performed rites and was very pleased with the resulting restaurant.
In short, I'd say major negative experiences and then logical sorts of reasons are much more likely causes. (Now, if you're talking about a hurricane, tornado, freak blizzard, or other "major negative experience" due to weather.. that's a different story.)