horses apparently are native to the region and are used much like horses have been used here on Earth throughout much of human history, from transportation to manual labour.
However, given how the Heavensturn event played out, they seem to have an almost zealous attitude towards them, even regarding other species which can serve the same role (read: chocobos), as 'inferior' - they refer to chocobos by the derogatory term of 'horsebirds', a funny bit of lampshading of a notorious incident that happened in 1.0's original release where the Chinese version of the client apparently indeed mistranslated chocobo as 'horsebird'.
It also seems the unicorns that are found in Coerthas are actually a separate species to horses, based on this event, although they both appear to be equines.