"Poor Old Horse" ("land" version) was used for house-visiting around the New Year in the latter half of the nineteenth century. The song seems to derive from a broadside ballad about an old horse, first printed around 1850.

The Maytime "obby oss" is something else entirely, being a native of the southwest rather than the North. I've never seen any evidence that either of them go back to "pre_Roman Britain", to "ancient pagan fertility rites", let alone to "the horse-cult, widespread in all Europe thousands of years ago" (nothing like upping the ante).

Here's a version of "Poor Old Horse", sung and played by a confirmed sceptic.