surfboards and cold temperatures

I don't know if this the correct forum to place this question but here it goes:

Does anyone know what could air or water can do to a surfboard/SUP?
In other words, can freezing temperatures harm your board?
Winter is starting over here in Europe and for the first time in years I really want to keep surfing during winter.
Also would there be a difference in reaction to the cold between a wooden or carbon board?

thanks

i get ice on my board if its on the car overnight in winter, can't see any harm, they do make ice boxes out of the same stuff.