That depends on the type of cast your child has. In general, casts are meant to stay dry. A wet cast can lead to skin irritation or infection.
Plaster casts and fiberglass casts with conventional padding aren't waterproof. Keep your child's cast dry during baths or showers by covering it with two layers of plastic, sealed with a rubber band or duct tape. Avoid swimming while wearing a cast that isn't waterproof.
A fiberglass cast that has a waterproof liner can get wet. Only certain types of breaks can be treated with a waterproof cast and liner. Ask your doctor if it's safe for your child to get his or her cast wet.
If the cast does get wet, you might be able to dry out the inside padding with a hair dryer. Use a low heat setting to avoid burning or irritating the skin.