A rear locker means you will be doing doughnuts constantly in ice/snow. It will not drive straight, it will always want to kick out on you. You have already mentioned the other big downside - when taking a turn, you either have to let off the throttle completely and hope that it disconnects (no guarentees) or stay in the gas and rip up your tires, not to mention get a lot of unwanted attention from the tire noise. I don't know of anyone that tows with something locked in the rear, but I would almost think it would be downright dangerous to do.
Unless you are wanting to drive it along the beach in the sand, you will have no benifits from it, I personally would just deal with a little bit of tire slippage at takeoff than go through the headache and expense of a locker. However, if you are deadset in doing it, look for an electric or air locker, something that you can shut off when you don't need it. I think you will find yourself never engaging it.