When a Horse Levels Up, the horse will receive a random ‘Max Bonus Stat’ and a ‘Current Bonus Stat’. The 4 ‘Max Bonus Stats’ are potentially either STA, SPD, DEX or INT, and the ‘Current Bonus Stats’ 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.