You might check with your vet, some equine veterinarians will do freeze branding.   If he doesn't maybe your vet can refer you to someone who does.

I'd go with the vet on this, or their recommendation.  Cattle are usually hot branded and that's quite the opposite of the look you're going for.

You might try local barns, a quick call might send you in the direction of the local brander.  Thirdly I'd try area equine clubs or organizations, possibly your farrier might know someone.

There is a fairly new outfit that branded my horse last Memorial weekend.  I was at the Buffalo Trail Ride.  They did a fantastic job.  Maybe you could contact BTR and they could geta number for you.

A place called Kryo Kinetics use to Freeze Brand horses, and the brands could be registered with the breed association.  If you want your horse branded for indentification purposes with a worldwide database, you might have to do an internet "search".  It's been at least 10 years since I had my Arabs branded by a representative of Kryo Kinetics.  If you just want a brand for the heck of it, call Buffalo River Trail Ride.  That guy was there last year at the June Ride.  I believe he was just a guy who would brand your horse for a fee.