Is it standard for graduate students to give their advisors gifts around Christmas, like chocolates or bottles of wine? What about other important people, such as their thesis committee members, or department secretaries?
No not standard (at least in Canada) and depends upon the tradition, it may actually seem as an odd thing. If there is a social gathering before Christmas then I believe that is fine to bring chocolates or whatever to all of attendees. I would be very cautious to give my advisor gift every christmas. A verbal saying before the holiday starts is normal and acceptable; nothing more nothing less.
A secretary is a different question. Especially, if they have been helpful to you personally, you can use christmas to show your appreciation. For example, when I first went abroad the deperatment secratary helped me with a lot of things that wasn't strictly her job (my health insurance for example). If (s)he is "just" good at her job but has not done something "special" for you, you can consider doing something together with the other collegues at your department.
The key difference is where you stand in the hierarchy: Giving "sideways" or "down" is much less of a problem than giving "up".