I don't like skinning before hanging due to the unattractive discolouration of the meat, but I tried skinning part way through the hanging period, thinking that the carcass would firm up a bit as it dried, making butchery easier.
The only result was that it made it an absolute bugger to remove membranes during butchery, as they'd dried to a parchment like consistency and stuck firmly to the muscle. I quickly reverted to leaving the carcass in skin until immediately before cutting it up.