Is there a facial cleansing method that is good for the skin barrier?

I am worried about the dead skin cells that worsen during the change of seasons and my skin starting to become rough. It is because my skin barrier breaks down as the seasons change. I used to think that my skin would improve just by washing my face properly. However, I found out that excessive washing during the change of seasons actually strips moisture from the skin layers and makes the skin even drier.

Is there a facial cleansing method that protects the skin barrier?

I use peeling products, especially because of dead skin cells. Can using the wrong peeling product result in damaging the skin barrier?

How about a foam cleanser with a peeling agent in it?

Dry skin and tightness during the change of seasons are really a tough problem.