Snowshoeing is great! Most ski areas have plenty of great (free!) places to snowshoe nearby, and snowshoe rentals are significantly less expensive than ski gear. It's easy for anyone to do (even my 68 year old mom), and still provides a healthy amount of exercise.
I really like both fatbiking (after intitial investment of bike, pretty low cost) and cross country skiing/sliding snowshoes i.e. Altia Hok skis with skins built in. Fatbiking keeps you in riding shape so spring isn't so harsh when it is time for regular biking again and doesn't need much gear other than the bike. Cross country skiing, espcially with a fat ski with a skin built in is amazing. Very low cost, and you can go just about anywhere as long as there is a little snow. Much faster and more exciting than snowshoeing and takes less skill than traditional nordic skiing.
Paultrusty, not only does fatbiking keep you in shape for summer riding, but after a winter of grinding it out in the resistance of snow and low-pressure tires, getting back on the road bike in spring feels like you've sprouted wings or somethin'! You feel like superman!
Down South, we never get enough snow to even considder skiiing. In compensation, we enjoy year-round hiking/backpacking/camping. Of course packing all those layers and other winter gear gets cumbersome, so I tend to lean toward car-camping more when it gets cold enough to need extra gear.
Snowshoeing and fatbiking are great, but I still like running in winter. I don't seem to have problems with breathing, even down to zero degrees F. I like going out and getting slapped around by the weather! Gaiters and nano-spikes are good options to have on hand for the feet.
Winter hiking and climbing! No bugs, no dirt, the air is clear and there crowds are generally nonexistent. With the right clothes you stay toasty warm (even at -50F windchill). I hike in the summer only to stay in shape for the winter.
Winter Hiking and Snowshoeing. Even trails that I hike all the time through the other 3 seasons look completely different under a blanket of snow. Walking across an empty field of snow that I know the rest of the season would be covered in trees and brush is just cool.