i've lived in Denver and commuted to work about seven miles each way for one entire winter.
long and short of it? it's pretty much the same as anywhere else, except it snows, and there can be ice. it only lasts for a day or two, but can make riding difficult.
and it can get pretty cold in the mornings, like zero F. type cold. nice part is that the misery, as stated doesn't last long.
i commuted on a friend of a friend's 60ish womens' three speed. so any bike will work.