Texas with a 2 month old

We are planning a vacation to Texas this winter around Christmas to see family, so baby will be about 2 months old. They want to take us to the coast and I'm worried about the sun. I'm a life long Wisconsinite, so not usually outside a lot during the winter unless it's not gross out. How do we protect a 2 month old from the texas sun? They're obviously too small for sunscreen, and I know that super southern Texas doesnt get *that* cold, so I'm stuck on how to dress baby and protect them. Any advice from Texas parents?