An article by INFORUM about the wild horses of Theodore Roosevelt National Park says the herd should not be smaller than 150 and may require up to 278 horses to reach 100 breeding animals.
Section 4.4.6.3 of the WHB Handbook puts the minimum herd size at 150 to 200 to achieve 50 breeding animals.
This does not mean that larger herds have lower risks of inbreeding.
The breeding population on the Maryland side of Assateague Island appears to be less than twenty.
On the Virginia Range, where the herd numbers into the thousands, the breeding population may only be a few dozen, because most of the mares have been poisoned by Zonastat-H.
Same for the Salt River, where the breeding population is probably in the single digits, or anywhere else the advocates are pounding the mares with pesticide-laced darts.
Under normal circumstances, breeding populations should correlate with herd sizes, and the risk of inbreeding should go down as the number of horses goes up, but if the advocates are involved, that model falls to the ground.
Western Horse Watchers Association 