If you're going to go out in the mountains in winter, learn about avalanches - where and under what conditions they happen, how to read a slope, and so on. This applies more to cross-country skiers, but a snowshoer might need it too.

But Paul is probably a better source than I am. Paul, do snowshoers need to know about avalanches out here?

Last weekend I went to Donut Falls in Big Cottonwood Canyon, though the path was clear enough that I didn't use snowshoes for the last part.

If you've never been to Donut Falls, I would highly, highly recommend it, anytime of year.