Frozen starter on 2004 silverado chevrolet

Hello!

Over the last few years, I had trouble every winter with my starter. Usually, after the first month of temperature under -10°c (14 °f) I was ok for the rest of the Winter. My starter gave up 2 years ago and I think it might be related to the temperature problem which cause humidity issues in it. I changed it for a brand new last winter and had no problem until today when it got close to -30°c (-22°f). It started fine in the morning but after driving an hour, I parked it then when I wanted to start again about 4 hours later, I had no crank so I started it by bypassing the current at the started with a wrench.

Is it possible the problem is somewhere else than at the starter?

If I cannot find any other cause, could I stick a heating pad directly on the starter or could it damage it? I have one that I is too hot to old in my hand and I would not want todamage it. I am pretty sure it would get rid of the humidity in it.

Thanks for your advice!