How to care for skin that is drier in spring?

It's spring now.

I thought my skin would improve as the weather warmed up in the spring, but I am worried because it actually feels like it is getting drier.

My face feels very tight after washing it, and I seem to get a lot of dead skin cells. How should I manage this?

I am also wondering if I should apply moisturizer more often, or if I should switch my toner or essence. Right now, I am only applying more moisturizer. Is this the right approach?

I would appreciate some advice on how to care for dry skin in the spring.