There's nothing overly problematic about using a winch on a hitch, but the same precautions exist regardless where you mount it. Main thing is to know the weight ratings of your equipment, know the weakest link, and do everything with safety in mind.
For a rear winch setup, the hitch itself—Class III hitches, like the ones commonly found on our trucks—may be the weak link, since they are usually only rated up to 6K. More importantly, that rating is for a straight pull; if winching on an incline, the winch pull could generate tongue weight, for which hitches have a significantly lower rating (maybe 600 lbs). It would likely be a fine setup for the scenarios you described, provided the vehicle is stationary and the pull is as straight-on as possible. That said, you should never drive the vehicle when the winch is operation, nor if there is a load on the line, unless it is to reduce/remove load on the line (and you're confident the movement will not inadvertently create tension, such as if the vehicle rolls back). The dynamic load created can be destructive, possibly deadly.
Other factors:
Remote wiring can be a little costly (low gauge wires run the full length of the vehicle, plus suitable quick-connects)
In-vehicle secured storage (presuming you take it on a trip and don't want to leave it in the hitch for any reason; leaving it installed will reduce departure angle)
Since you mentioned snow/ice pulls, you may also want to carry some chocks. Again, the vehicle should be stationary when pulling. Otherwise, a snatch/kinetic strap/rope is warranted.