When a Horse Levels Up, the horse will receive a random โMax Bonus Statโ and a โCurrent Bonus Statโ. The 4 โMax Bonus Statsโ are potentially either STA, SPD, DEX or INT, and the โCurrent Bonus Statsโ are either GAT or TMP.
For example, assuming your horse is Rare and Max Level 14, that means your horse can increase its Max Stats and Current Stats, up to 13 times from Level 1 - 14. This means having a Common horse doesn't mean you'll always lose. So, talent can be defeated by using judgement, training and care in raising your horse.