I've been in Florence in November twice - once with my husband in 2016 and once solo in 2018. (Still have the husband - LOL)
I live just outside of NYC so I am used to cold, damp and snow, Neither time did I have that. It did rain a bit in 2016, but I wouldn't call it cold. Dress in layers and have shoes that can get wet.
I am a huge museum person (former full time art curator and present consultant) and loved having the Firenze pass. Yes, it's pricey, but it allowed me to pop in and out of places and not worry about lines. The morning I went to the Uffizi Gallery in 2018 I was the 3rd person in line and spent a lot of time alone in galleries. It was glorious. The crowds are low, you can still sit outside, and the Christmas lights start going up by the end of the month.
I took three "day" trips, although one of them doesn't really qualify as a day trip. I took the bus to Fiesole (20 min) and walked around a bit, looked at the Roman ruins, and came back down the mountain to the city proper. It was foggy that day so my photos were great but the views were not. I also went to Ravenna (long trip but I didn't care - I needed to see those mosaics!) and to Siena (easy and cheap 1 hour bus ride).
I personally think the Duomo museum across from the Duomo is one of the best museums I have visited - anywhere. And I travel a lot.
A week in Florence is wonderful and I would do it again in a heartbeat.