Zorses may have evolved on the plains of the Jogos Nhai. There is no mention so far of anyone in a khalasar riding a zorse. In Qarth a pair of Jogos Nhai presented Daenerys Targaryen with what she describes as one of “their” zorses, which could possibly mean that the Jogos Nhai people are associated with the zorse, as the Dothraki are with horses, but this is mere conjecture.
Zorses are ridden by members of the Brave Companions and were likely transported to Westeros with the sellswords as their personal mounts when they were brought by over Tywin Lannister.  Thus far there has been no mention of any other sellsword companies having zorses.
As a highborn child Arya Stark received a good education and is well acquainted with horses but she was still not able to identify the zorse by name when she first sets eyes on some of them,  so presumably they may be unknown among even well-educated Westerosi and remain very rare beasts on Westeros. The differences between riding a zorse, as opposed to a horse, is not known. Dany has ridden with the Dothraki so if she thinks the zorse fierce it should be safe to say that they are more aggressive than horses. The Dothraki opinion of a zorse is not known, other than to say they do not seem to favour riding them over a horse.
A Game of Thrones
A Clash of Kings
In Qarth a pair of Jogos Nhai present Daenerys Targaryen one of their striped zorses, as a token to the Mother of Dragons. She describes it as black-and-white and fierce.  Dany sells the zorse along with other gifts received in Qarth in order to gather wealth needed for petitioning Pureborn. The only gift that she keeps is the crown given to her by the Tourmaline Brotherhood.
References and Notes