After the last big hurricane that hit Galveston, I was wondering if there are many homes even in the area. I saw pictures of the waterfront neighborhoods north of there and there were just a house here and a house there still standing. Communities essentially disappeared.
My cousin is a professional engineer out of Houston specializing in mold abatement. He had a big year after the hurricane as every commercial building down on the coast had to be inspected. And there were problems everywhere along the coast.
If you can find a place to stay, go for it. Or, go south to the Corpus Christi area. Texas weather is pretty good even in Winter.