Are there any good exfoliants for dry skin?

My skin is dry, and when the seasons change, dead skin cells build up.

I'm worried because of this. The breakouts are particularly severe only along my jawline and around my mouth. I bought the Shure Pack before because I heard it was good, but sometimes my skin felt tight after using it, and it felt even drier in the winter, so I didn't buy it a second time. For those of you with dry skin like me who have severe dead skin cells, what products do you use to manage it?