Since no one who's actually tried it has replied yet, I'll just give my two cents.
At least with a trike you don't have to worry about falling over but there are a few concerns I'd have about using one in the winter.
1. You've got to push two tires through the snow instead of one
2. Availability of studded tires in the appropriate size
3. Wider footprint
Studded tires don't help on snow but anyplace you have the potential for snow, there's the potential for ice.
The wider footprint may not be a big deal except that sometimes I find it easier to ride in a tire track and you could never get all three wheels of a trike in the same track. Also I just like to be "skinny" when there are cars going by me. Being lower you're less visible anyway and it's darker in the winter which compounds the problem.
If you do try it, please report back.