It doesn't apply to non-humans because herd immunity is not something that is at all related to non-human populations. The term was coined to describe a trait of human populations and was found to be difficult if not impossible to achieve in humans until we started to vaccinate.

https://en.wikipedia.org/wiki/Herd_immunity#History

When cows get mad cow, you quarantine and then kill potentially infected cows. Wild horses have behaviors. They may not change their behaviors when they find a virus, but that doesn't mean that the reproductive rate is independent of the horses behaviors. It absolutely still is.