Of course there are horses in hardcore mode. The only things that happen when you set a world in hardcore mode is you are trapped on hard difficulty, and you have 1 life. If you are not finding any horses on your current hardcore world, that is because it was generated before 1.6. Horses only spawn in plains generated in 1.6, so either start another hardcore world, or generate new chunks.
WoM Coins: 1712
Of course there are horses in hardcore mode. The only things that happen when you set a world in hardcore mode is you are trapped on hard difficulty, and you have 1 life. If you are not finding any horses on your current hardcore world, that is because it was generated before 1.6. Horses only spawn in plains generated in 1.6, so either start another hardcore world, or generate new chunks.