It collected frost but also became slippy as hell, even with the frost taken off.Is that because the handle froze? I use vegetable oil, which doesn't set but when it's cold it turns into something like a wax. I've also been favoring the saw in colder weather. I've been having trouble with axes. Aside from chipping, when you warm them up enough to function, they start accumulating ice on the head, which is a nightmare to remove. That's not even in extreme cold. In my area it almost never gets below -20C. I'm sure there are some tricks to use them under such conditions, but I haven't found them.
I've been advised to wrap it in tennis racket or bike handlebar tape. I'd like to see what Lemon oil is like at low temps, its fantastic for tool handles at normal temps.
As for ice build up, I reckon your not swinging it hard enough