If those estimates hold true it's going to be a cold November with some nights being very close to freezing.
What is open at that time of the year on the Vadiniense. I expect one of the albergues or campsites in Potes, maybe. Possibly the refugio at Fuente De, but on the other side, will anything be open between Fuente de and maybe Cistierna? I'd still carry a tent as there are two possible campsites on the other side, Alto Pico and Riano. Alto Pico comes across as camping in a field next to someones house with basic facilities, so they might be up for someone in a tent having a night, but don't know for Camping Riano, well not until about September the 7th when i hopefully stay there, but it looks pretty mainstream. They both have websites.
If the OP decides to walk, I wish them luck. I have enjoyed a couple of winter mountaineering experiences in the past and walking in snow in mountains can be a lot of fun, but also hellishly dangerous. But as the younguns say, YOLO.