Only ridden there in the summers, but I have a bunch of friends on another forum from that area. Occasionally see facebook posts about someone who braved it out on a warm day randomly during the winter, but it's usually to work and back. Mountain passes can have snow LATE in the year, and are pretty much only car or 2-wheel drive Ural with sidecar passable in winter.
Red Mountain pass, 5 June 2010:
Same location, 1st weekend of June 2011 (note the giant snowpile behind us):
Oh, and the road that pass is on is definitely worth riding. The 'million dollar highway' as Hwy 550 is called, specifically the section between Durango and Ouray is breathtaking.