[chryuop]

Ladies and Gentelmen...I am going to make fun of myself!
But I will try to explain it...
隠す (かくす) is a transitive verb and means "to hide". Thus as a transitive verb it requires the を for what it is hidden. I wouldn't see it as "hiding from something", but more as "hiding your self/your body to someone/something". If you think it this way 雨に would represent what you are hiding from.
Always in my opinion (that I repeat might be as well be wrong) if the rain is the place where you are hiding from something or someone, than it would become a place where the action takes place, thus requiring で.
So the way I see it is...
私は雨に自分を隠す　I hide myself from the rain.
私は雨で彼に自分を隠す　I hide myself from him in the rain.

But wait someone with more knowledge than me to confirm or correct me.