Snow provides a fine surface for ultimate frisbee, and winter tournaments are easy to organize because there is (usually) snow everywhere.
Many events are "Hat Tournaments", with Russian and international players of all skill levels welcome. On other events there is always a pick-up team that you can join.
Winter is a great time to visit Russia. Airfares are at their lowest, and tournament organizers can often help you to find a cheap or free place to live.
Here you can see the tournament schedule.