Just equining or buttocking around

[Douglas G. Wilson]

The conventional US slang verb "horse [around]" = "fool around"/"play
boisterously" apparently dates from about 1927.

One might suppose that this is derived from "horseplay", an old word (OED
gives 1589).

There is an equivalent verb in British use: "ass [around/about]", from 1899
(OED).

The (presumptive) variant "arse [around/about]" is cited in modern times
from 1922 (OED).

A solitary example of "arse about" however appears in the OED as "obsolete"
[amended in the supplement], from 1664!

All three apparently are in current or at least recent use.

What is the relationship?

-- Doug Wilson