Lots of folks use short fast bows to hunt here, just not necessarily Asiatic style (better term than horsebow).
Asiatic bows are fun and very fast, but not as popular as the reflexed riser and siyahs are not as user friendly to average Joe. You can probably get 99% of the performance from a short static recurve with a deflexed riser, so in the end it comes down to personal preference. I've owned several Salukis and a Hwarang and while fun and effective in their own right I'd take something like a 54" Shrew or Javaman Helms Deep or short Centaur 9 times out of 10 to go into the woods with.