Boy, from the looks of that photo she doesn't look all that fat to me. We have a couple of Paint easy keepers. One is a mare I bought last spring who was overweight. Off lush pasture and on grass hay and literally a handful of Sr. Feed with her vitamins she has slimmed a few notches on the cinch. Both Paints are blocky and full bodied as opposed to my leggy, slender Arab/Saddlebred.
I would be concerned about free-feeding an easy keeper.
You might have your vet check her over. I think it is always good to have a vet familiar with a horse because sooner or later you will probably need one and they will have a base record to refer to.
Good luck. She looks like she will be a nice girl for you.
If you ever find yourself in a fair fight, it's because your tactics suck. ~ Marine 1SGT J. Reifinger