Horses have 4 stats: Strength, Speed, Stamina, and Temperament.
Speed and Stamina are pretty straight forward. Speed, is well, how fast you can go, and stamina decides the number of times you can boost the speed before it has to rest. Temperament is explained in this Q&A.
But what does Strength do?
Best Answer
Based on the information collected in this Reddit thread, it appears that the Strength stat of a horse does, indeed, affect how much HP it has.