Winter means such different things in different parts of the world and at various elevations. Also, the likely number and size of the people in the tent is another obvious factor. If 90% of the time I'll be sleeping solo in my tent, and the other 10% of the time with a SO, then I'll be looking at a much smaller tent. During the winter I find that I take up an even smaller amount of space than during the summer, because anything I don't want freezing is in my sleeping bag with me or under me for extra R-value on the snow. You might think you'd need more space, due to the extra gear and general bulk, but that has not been my experience.
As others have mentioned, if you're at a relatively low elevation where you're unlikely to get much snow or high winds (and often wind can be mitigated with good site selection), a 3-season tent could be fine.
At the next level, you could consider some of the "all season" type tents, like the
REI Arete ASL 2. It's not a mountaineering tent, but seems like it would do well in most winter backpacking conditions while not being as expensive as many of the mountaineering-type tents. Another option here would be some of the various pyramid tarps like the GoLite Shangri-La or BD Beta Light.
If you're looking for something that's (a) more of a winter backpacking/mountaineering tent and (b) for one or two people who don't mind being cozy, you could consider the BD FirstLight or Mountain Hardware Direkt 2. In deeper snow you don't have to dig out as big of an area, since they have small footprints. They shed snow and wind, and are pretty light and inexpensive as 4-season tents go. My girlfriend and I use a FirstLight during the winter months, and it's been working well for us. I like the small, cozy feel.
If I were planning a multi-week winter expedition to Alaska, I would most likely spend the money on an BD I-Tent, Fitzroy, or something in that category.
Hope this helps a bit. Good luck with your purchase!