You can use an antiseptic like chlorhexidine or cetridine or betadine on your cat with no problems so check what you used on your horse. I would use betadine as a last antiseptic though - flush with one of the others or saline first. If it is a bite wound it really needs to be seen by a vet - firstly because it is likely to get infected quickly and potentially badly, secondly because dog bites can do a lot of damage to tissue that isn't always visible at the skin level. Hope this helps.