For people unfamiliar with running snowshoes, the first image that might come to their mind is the great big wooden snowshoes with a long tail and webbing made of animal sinew. Those snowshoes have their place, but you certainly can't run in them. The snowshoes that are made specifically for running are much smaller and lighter, and you can maintain pretty much your normal running stride when you wear them.
Another advantage of running on snowshoes is the grip- most running or hiking snowshoes have metal cleats under the ball of your foot and your heel, which allows you to run safely across slippery surfaces that would be treacherous in even the most aggressive trail shoes.
Don't let winter chase you away from getting outside and enjoying nature. Snowshoe running and racing can be a great compliment to your regular training, and it's a lot of fun.