'Horsey Keep your Tail up' was a popular dance band number in the 20s and 30s. According to Michael Kilgarriff (most Muddies would find his 'Sing Us Oneof the Old Songs' OUP 1998 really useful) it was written (written down?) by Walter Hirsch and Walter Kaplan and published in 1923. The tune I remember well was not the one on the Joe Offer link.