We should post up a petition in Suggestions that forbid and dump override ownership. Those discarded clothes always kind of irritated me too
Two things I'd try - first, set the wrestler to armor level clothing - you might want to place the dwarf on duty first or change weaponry to crossbows to prevent no-armor sparring. Each time you cycle from plate to clothes there is a chance that dropped clothing will be picked up and worn.
Yeah, say there are a couple mittens in your barracks. If you determine the owner and set armor level to clothing they should put that item back on after they've shed their chain mail, etc. However, as soon as you reset their armor to chain or plate, they'll very likely end up dropping that same piece somewhere else.
This is mostly an issue with shoes. When a dwarf gets a new piece of clothing or dons armor, they just put it over whatever else they are wearing. With the exception being shoes. Dwarves take off their shoes to put on either a new pair or boots. Mittens seem to be another such exception. If your dwarf spawned wearing gloves and mittens, they'll shed the mittens when asked to wear gauntlets.
If this doesn't work try stripping the dwarf of all jobs and de-activating. That way all the dwarf has on its plate is eat, drink, sleep, and store owned item. Note that this option is not available for highly skilled veterans (heroes/champions).
Generates the same problem as above. When dismissed from the military, your dwarf will put his mittens or Xalligator leather shoeX back on. Which will be discarded again as soon as you draft him back into the military. Also dwarf needs a bedroom (and preferably a cabinet) to get a
Store Owned Item job