By my reckoning, the Yorkshire Garland Group has two mummer's songs, Poor Old Horse and Six Jolly Miners, both from North Yorkshire: https://www.yorkshirefolksong.net/song.cfm
Calderdale's Long Company Mummers have both a wassail and a calling on song; I'm not sure of the provenance of either, but the latter has the feel of a song that may have been written by Pete Coe. I'll try to ask Johnny Adams tomorrow! https://youtu.be/yqDqIIOcPiI?si=ZnK97qLCAaAnBhtS