Horses, zombie horses, skeleton horses, donkeys and mules still use the old, brown, "Horse saddle"/Mo' Creatures by DrZhark mod’s texture.
This is clearly visible when comparing to other mobs with saddles, such as pigs, camels, striders, ravagers and the saddle item texture, which appears to be more orange in color.
This issue is already tracked and resolved as Working as Intended in MC-181530