Snowshoe running has experienced an explosion in popularity over the past few years. You can enjoy a vigorous workout or bask in beauty and solitude. The soft surface minimizes impact and develops strength in the leg muscles.
Snowshoe engineering has improved substantially making show shoe running much more enjoyable. As with cross country skiing, don’t forget mountain safety, be prepared for adverse conditions.
I have not been able to find research comparing snowshoeing to running. If you are running with snowshoes the training effect should be very similar to running. Since you can not run as fast on snowshoes, race times would probably not improve. However, snowshoeing would be a tremendous way to improve strength, power and overall fitness while minimizing impact and enjoying the beauty of the mountains.
A great site for everything you could want to know about snowshoe running is www.snowshoemagazine.com.