I just clean them out and use a thick cream like vitamin E lotion. It's good for promoting healing and growing back hair.
If you are in the U.K. a cream called Camrose is great for fresh cuts and scars.
I had a horse years back that was burned by the clipper and left a long scar. It took two years of application but the then 50cm long scar is completely gone.
We use a Fura-zone cream on our horses
"Cicaceptive" by Equibao or Aloe vera gel :)
I use Silver Ointment when my horse gets a cut. It helpes to suppress bacterial growth and helps the cut to heal faster.