Hitch is in the center and I doubt it would make any contact with tires... front or rear.
It would hit everything else... completely change your approach or departure angles.
It's why we mount them on top of or inside front bumpers.
Now...if you used Anderson connectors for the power...and removed the winch every time then much less of an issue.
I have a 3500 lbs ATV winch with 1/4" synthetic cable. I've occasionally used it on the back of my Jeep with a recovery ring. The winch plate it welded to a receiver since I couldn't find anything as small as I wanted.

-Mac