Old home with closets that get damp in the winter.

My wife and I live an old home. Our closets are both situated in corners with 2 of 4 walls being exterior walls.

In the winter when we kick in the heat or when we experience massive temperature fluctuations, our closets and clothing get super damp.

Any suggestions? We’ve used damprid moisture absorbing buckets in the past with some success. Is there anything else we can do other than redoing the insulation?