Is there something I could put on a fleece blanket to make it water proof?

You should be able to buy something like Camp Dry in the sporting goods section of your fave store. They'll be able to help you more than anyone here, you can even take the blanket there to give them an idea of what you're dealing with. If you have a camping store in your area, even take it there; it may take several applications and/or be an expensive application, but I'm sure that it's doable!