Wild horses have a keen nose for water, which includes sources underground, according to a report published yesterday by National Geographic. Water holes created by the horses also benefit wildlife.
The story refers to them as an introduced species, suggesting that they’re not supposed to be there, but reintroduced might be a better choice.
A Wikipedia article about the Banker Horses provides another example.
Is the behavior limited to the wild?
This hole was dug by adopted horses in their corral. Water is added manually for them to play in and curb their interest in digging further.
Western Horse Watchers Association 