Weather depending mind
Ha ha, yes! Would that be sideways rain or the usual vertical type

Mind you it can be icy at that time of the year too. Not wanting to put you off, but I broke my collar bone after crashing on some black ice a few years ago at that time of year.
To be honest, you'd be hard pushed not to find anywhere nice to cycle around there. The roads are quieter than the main roads in and out of the honeypot villages anyway. Although compared to most other places I'm sure it will still seem quiet on the road especially at that time of year

The only road I'd avoid is the A592 between Newby Bridge and Bowness. Its a very fast moving road with a lot of traffic, narrow in places too.
A lap of Lake Coniston is a nice ride, especially the road that skirts the east side of the lake. A good 'out and back' would be to go up to Chapel stile, maybe over to Grasmere. Another nice ride would be heading south to Grange over sands. Taking the left hand turn just over the river Leven bridge on the B5278 takes you over Bigland Hill and drops you down into Cartmel and then over the next hill into Grange over sands. It's a bit of a stiff climb up bigland hill but the views are worth it at the top (the view will be behind you though!) Both Cartmel and Grange are lovely spots for a stop (Cartmel if you prefer a beer, Grange for Cafes)