Just state that you are trading horse "so and so" for horse "so and so". If its a straight across trade, then say "no money has been exchanged in this trade.
Describe each horse, registrations numbers if they have them, have both you and the other owner sign them, and its done.
When I traded my gelding for a mare, we just gave each other the signed registration papers and brand inspections and that was it.
It's also very common in the horse business in general to add "As is" on bills of sale to protect against folks coming back later and saying they want to 'un-trade' because something is wrong with the horse (whether true or not).
Try Googling "Horse bill of sale" or "Livestock bill of sale" and see what you get. That's what I did when we sold some cattle and I needed the bill of sale for tax purposes. I would definitely execute some sort of document regarding the trade.