My training (that is, putting in a good effort, getting the heart rate up, hill reps and such) is really limited by snow and ice rather than temperature. In the cold places I've lived, snow and ice usually tend to turn up around 20F.
I'll ride at temperatures below that, but it tends to be slow and technical. I'll do hills on studded tires, but the game is as much about keeping traction as it is getting up the hill. As a result, rides tend to be much slower and easier (from a fitness point of view) and more about getting out and enjoying the sunshine than keeping up with a summertime level of fitness.
Sadly, the trainer is the only way I've found to keep fit when all the roads are covered in ice and snow. Running or cross-country skiing would probably be good options, but I don't do that.