The pads left some clumps of horsehair and an overall "patina" of miniature squares of fiber. It doesn't appear the mats were glued down, just that they stuck to the floor over time.
I've only gone so far as to try a damp, mildy abrasive pad and elbow-grease. The bulk of the clumps were generally removed (although not as much as I'd thought they'd be) but the miniature squares were relatively untouched.
We don't want to resand and refinish the floors, but just want a solution to make the floors less "hairy." (Although I wouldn't be surprised if resanding were our only option: this stuff is stuck on there!)