Does a 3 season room count towards square footage?

Usually no—it typically isn’t counted unless it’s fully enclosed, permitted, heated/cooled, and finished to the same standard as the rest of the home.

Heated/cooled space is usually included in your total sq. footage. Although a screened porch is added "living space" it is not calculated as such. An increase in your sq. footage could result in increased property taxes for you (or for the new owner if your property is being sold).