The purpose of the 30 day notice is so that the boarding facility has an opportunity to find replacement income (another boarder) in the mean time and not be left without income that they had planned on having. If you have already paid, it actually works out better for the boarding facility that you are leaving.
That means they have been paid for services that they don't have to provide. Move your horse ASAP. You'll be fine.
Proud owner of ~Mana: 6yo Arabian gelding~Pearl 13yo Arabian~Danzer 14yo Arabian mare~ Tiny mini filly