If they are healed, they shouldn't count it against you.
Now, if the cut was recent, they could take points off if it looks as though you have done nothing to care for it. Alyssa_1st_horse_show_06_30_10_0273.JPG
^ Joey literally sliced his skin off his leg two months before he was shown in Halter. My instructor did everything in his power to make it heal, but there just wasn't enough time for it to completely heal up. So we put a pad over it and wrapped it in pink vet-wrap to make his leg look cleaner.
The judged asked me what happened to his leg and how we were treating it, and I told her, but hse never marked me down for it.
The judge may ask what happened, but with scars I don't think that will be very likely.
EDIT* Another thing I will add is I don't think a little scar is going to matter unless your horse looks like he had been thrown into a blender. That may cause you to lose points.