the walk cycle of the elephant can be transferred to other animals (including the p4 horse) with with puppet master, as could the trot and the gallop.    that would cover walking and running (as per your subject line), and i thought that was what you wanted, but you seem to want something much more specific.  and, oddly, HaiGan and EdW's freebies seem to have vanished, and they had many horse related freebies.  when i get home, i can tell you the walk cycles i have and for which animals and any readme info, but i can say now i got them all here.  why they're gone, i don't know.  but it probably wouldn't matter, because if you don't like the dragon or elephant walk cycles, i doubt you'll like any of the others because they're all pretty much the same: basic quadruped walks and such.  if you're looking for a specific style, then, yes, you'll probably have to make them yourself.  i'm not sure what's needed to be able to bring the cycle into the walk designer to adjust instead of by hand but i can suggest consulting little dragon, nerd3d, and using ockham's animation python scripts (emphasizer, et al.) for tweeking.

maybe someone else will point you in a direction you find helpful.  good luck!