There is a similar creature in Finland called "nuuttipukki" - back in the day, young men dressed as goats (inverted fur jackets, birch or bark masks and goat horns) would travel from house to house and demand food and alcoholic drinks from their hosts. If they didn't get any, they'd make mischief in retaliation (there's tale of breaking down fences to let cattle escape into the woods).
They usually made lots of noise as they traveled, though they weren't the singing type like the Mari Lwyd; instead they'd just rant and roar and basically be super scary.