Cost and work involved in keeping horses would be a major reason I would think. I'm no expert though.
I know a guy in Idaho who ran outfitted mountain hunts utilising horses. Many horses. Visited his place once and asked where all his horses were ... I couldn't see any on his ranch. Told me he leases his horses seasonally apart from a very few kept for use by he and family. Looking after a herd of horses is a full time job and he didn't have time and couldn't afford to employ people to do it.
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