How many degrees is the sun above the horizon in the winter?

That depends on the latitude from which you are observing Polaris.

At the Equator (0 latitude) Polaris will be tangential to the northern horizon (0 degrees of altitude)

At 52 degrees north the altitude of Polaris will be 52 degrees

Therefore At the North Pole (90 latitude) Polaris will be overhead (90 degrees of altitude).