Snow is beginning to fall here in Utah
So I'm thinking of snowshoeing. Here is a nice panorama I took last year atop Mount Olympus just outside of Salt Lake City, Utah. This is an excellent hike most of the year. The winter doesn't necessarily prevent you from hiking here. However, it's not really doable Dec. - Feb. unless you're up for an adventure and soggy pant legs.
I say take: 1) solid hiking boots 2) Yaktrax for the lower half 3) snowshoes for the upper half and 4) a backpack for storing your layers. You won't want a winter coat till you're nearly at the saddle before you summit the rocky peak.