For pure cancer rates, no, it's still a relatively slow progressing disease and a cancer may grow more in the winter only to be diagnosed in the summer.

I guess you could look at cancer growth rates during winter/summer, however we live in relatively controlled environments. I don't think you could control for AC usage / how much time you spend outside versus outside.

Living in a climate where buildings and clothing are adapted to cold, I rarely find myself cold enough to shiver, so I'm not sure there would be much difference. People actively avoid cold despite the weather.