I think that in Ireland wrenning was practised mainly by boys. It was partly a way of getting money (hence the decline of the custom in direct proportion to the increase in prosperity) but also a way of impressing the lasses.

Variants of this custom are known in England. In one place, instead of "the wren, the wren, the king of the birds", the merrymakers would process with rams' horns, reciting "the ram, the ram, the king of the Jews". I don't know what distribution of ages was among those who practised this custom.

The wren is one of the more common birds that winters in northern Europe, so it isn't surprising to find numerous literary and musical references to her. (Her American cousins are just as spunky and fine.) Even if the Cindy Mangsen song is new, which it may be, it sounds from your description like a combination that incorporates some traditional components.

T.