Your best bet is to have the TV viewable through a window in the closet. The window will need to be an insulated glass type so fogging and sweating will be minimized. Installing a window in the closet will be much easier and will let the TV breathe. You will need weatherproof speakers and a small amp to run them. If you can go ahead and tie the house audio in as a bonus.
Don't forget the waterproof remote too.