Urban dictionary, surprisingly, has a definition for 'Hair in a braid':

'Enjoying the festivities with the maximum enthusiasm, being the life of the party.'

Of course urban dict isn't exactly merriam-webster, but it seems to fit the context here. I suspect it's American slang but either way it is not a very popular expression on google.

The second bit - the song - I always just took to mean 'with evident cheer'. Might well have missed the point though.

Isn't Wodehouse's terminology great?