There might be too much oils & waxes in the bridle leather for the paint to adhere.
You might need to use acetone on the letter areas to be painted. Take a piece of scrap bridle leather & stamp it, then rough & clean the area with acetone & let dry for a day then paint your letters/leather.
Might need to use a solvent base paint to, I am not sure. But curious to see what the answer is.