There is a famous genre of tune in Japan, "packhorsemen's songs". These have been elaborated far beyond anything a working horseman could possibly have sung, with wildly complex instrumental variations. One of the commonest types is called "Esashi oiwake" (there must be YouTube and Spotify versions but I can't look for them right now).

The most elaborate horse tune in British tradition is probably "John Paterson's Mare" aka "The Black and the Grey" - long set of variations in the William Dixon Manuscript. Not in the same league as "Esashi oiwake" though.