What SpirtWalker said. But it depends on what you're up for. I've known more than a dozen CDT SOBOers or more including myself who were still in CO in mid Oct. Heck, I didn't get over Wolf Crk Pass until Oct 2? on a CDT SOBO thru. Yeah, there was snow but mostly still clear and manageable southward. Maybe, I got lucky.
This tells me you may be up to it providing.... Nov is getting too late to be hiking the CDT in CO without it involving snow travel for a continuous 200-300 miler. You'll likely on a 250-300 miler get snow to some extent being out there on the CDT even in NM but again it depends on your CDT route. SOBO CDTers are still in NM in Nov. I didn't finish until, if I'm recalling correctly, Dec 3 but I was doing many ridge lines and sometimes alternates as well as the official tread. As said sunsets were spectacular. Days were short. Hiking after sunset was common. Water wasn't all that a big deal, because for one thing I researched the hell out of it for my NM CDT time frame. It was a solitary experience as a SOBOer in 2010 with, to the best of my knowledge, only 7 total going SOBO. I'm also of the opinion NM in mid Oct - mid Nov maybe early Dec depending on where I'm going is GREAT, maybe optimal cooler weather hiking.
I absolutely disagree with this statement though, "obviously late fall is not the ideal time to be backpacking out west" as it depends on where one chooses to hike. However, hiking the overall high elevation avg of the CONTINENTAL DIVIDE Tr may not be the best. Heck, you're in the southwest corner of CO. WHY does it have to be the CDT you only consider when you don't have to travel clear across the country to get in some FINE 200 -300 milers in in New Mexico, Arizona, the coasts of Cali and Oregon. Then, if you're willing to stretch out traveling distance to the mid south, southern Texas, such as to Big Bend and a combined Guadalupe NP 200 miler, or a thru of the Ozark Highlands Tr in Arkansas you're good weather wise. I'd say possibly optimal weather wise for a mid Oct - mind Nov foray in some of those places.
Other good possibilities include picking 2oo-300 miles of the eastern Grand Enchantment Tr OR 200-300 miles of the southern and possible mid AZT OR combing some miles of both making up your own hike sampling 300 miles total of both trails. The Superstitions are beaufitful temps at that time. All this is possible for you being based out of Telluride awaiting ski season to crank up in earnest. Show up on the slopes with a AZ or NM tan. You know you're going to be opening the door to some female companionship and discussion doping that.
I would really like to see more hikers breaking out of a limiting mindset that relegates them to only the Big 3 TC trails, maybe the Big 4 if also including the JMT, when considering hikes, OR east coasters assuming Florida is the only place suitable for late fall and winter hiking.