Some people don't perspire much in cold weather. I know I do, now matter how cold it is, assuming I am dressed appropriately. For me this means fewer layers than most people, so I do not over dress. If your top layers are mostly zipper-equipped, and you actually heat up because you are pedaling hard and you have on many layers, opening one or more zippers can help retard perspiration. What gets anyone cold, of course, is sweating under those layers and then having to stop, as when marking timing points. Keeping dry as possible with wicking fabrics and lots of zipper management keeps down the sweat and then the danger of rapid hypothermia for me.
As a novice runner, back before I knew about the risks of getting sweaty on a frigid run, I ran for 2 hours in 15 degrees F in a cotton sweater and a light windbreaker. I was fine until I finished, stopping my run about 300 yards from my car. I was soaking wet but warm. By the time I made it to the car, I was shaking so badly I could hardly drive. I nearly passed out before the car heat came on. Less likely to get this way on a bike ride, I assume, but still possible if you are over dressed and you can't unzip enough layers.
Wear a ski mask.
I would like to hear how it went. Stay safe.