There are two different types of weather in Survival 404. Storms, and Sunny. This'll be explaining both.
When it's sunny out, your character is pretty safe. Because this isn't a storm, your character can walk freely without losing health. This is a good time to do just about anything.
If the storm strikes, you're in for a bit of trouble. During a storm, your character loses health at an average rate of your hunger. Unless you're safe and sound inside a building, your character will be buffeted by the storm. It can get pretty dangerous if you don't pay attention to your health bar.
Crude Hut: Wall + Wall + Med Foliage
Mine: Wall + Med Rock + Med Rock
Large Hut Parts: Wall + Wall + Large Foilage