Where are all these hypothetical horses in Tyria? During my play through GW1, and my experience in GW2, I didn't see a single horse. We could probably stop here, and just conclude "There are no horses on Tyria." But, there are a few things that lead me to believe there were once horses on Tyria.
Firstly, there's the Iron Horse Mine in the Shiverpeaks. While this is, admittedly, very weak evidence, it does tell us one thing. The local denizens have some understanding of what "horse" is. The term "iron horse" of course refers to the industrial machinery that first replaced horses as modes of transport and beasts of burden. If the term exists in Tyria, surely horses must've been around, somewhere, at some point?
Then, we take a jaunt south to Cantha. See this excerpt from Loremaster Ermenred's An Empire Divided,
[Kaineng Tah's] death came from an unlikely event: while on an extended hunting expedition, his favorite horse improbably threw Kaineng Tah. It is doubtful that the faithful, well-trained beast would have done this out of belligerence, though Canthan history does classify the death as completely accidental. It seems more likely that one or more of the emperor's fellow huntsmen spooked the horse. Fragmentary records of an unexplained wound on the horse's rump and three more such wounds on Kaineng Tah himself would appear to support this interpretation.
His son, Yian Zho, was also said to be a skilled horseman.
Assuming these two references aren't just unfortunate oversights, this means at the very least that there were horses on Cantha as late as the 5th century BE.
So, the question is, where have they gone? Did they somehow go extinct? If they are extinct, what drove them to that point? If they're still around, but out of sight, why are they hidden? Speculate away!