We often camp in the mountains of Colorado through the middle of October, which seems to about be the cutoff. For years, we had a standing "date" with our friends to camp at Grand Lake the second weekend in October. Once we had an inch or two of snow, but otherwise just cool, crisp, gorgeous autumn days. What I'm saying is there's a chance you might hit snow, but it won't be too much unless we have a very rare big snow event. Heck, one time we were chased out of our camping spot on the 4th of July by 6"-8" of snow when we awoke in the morning and it was still coming down so hard it was tough to see. It was a gravel road and we had to use 4x4 for miles to get out! So any month of the year . . .
I'd stick with US 50 over Monarch as I-70 has two high passes to go over, not just one.