Is it standard for graduate students to get gifts for their advisors? 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.