I did just a little surfing of the literature and found a bunch of papers, albeit a bit old from the 80s and 90s, that suggest that dumping is not the issue I thought it might be - which also means the problem is more difficult. Most studies of horse population dynamics are reporting per capita rates of growth in the 1.15 to 1.25 range, which is truly huge. Annual survival rates for adults run well over 90% and efforts at cropping the populations, for some reason, focus mostly on males which doesn't help much either.
Overall, horse populations are very self sustaining, and dumping, seems to be pretty irrelevant to the problem.