Elk Tooth is a long haul in winter!!! Snowshoes, oh yeah! I'm not even sure it could be done reasonably in a single day. Climbing up gullies is usually not a good idea in winter as they're apt to be full of unstable snow. Not something to try to bite off if you haven't done much in winter. There's tons of better options... although I must admit Elk Tooth is a very cool peak!