The Catalog of Copyright Renewal Records (1963) has the following listing on page 938:

 DALY, ARTHUR J.
    Horsie, keep your tail up, keep the
      sun out of my eyes, by Clarke Van
      Ness, pseud. of C. V. Clark, and
      Arthur J. Daly.  (In Clarke's
      comedy song folio)  © 25Sep35;
      AA191563.  C. V. Clark (Clarke Van
      Ness) (A); 14Mar63; R312349.

The Online 78 rpm Discographical Project lists the following records:

Okeh 40107; Chubb Steinberg Orch; HORSIE KEEP YOUR TAIL UP; recorded 4/10/24; composers: Walt Hirsch, B Kaplan.

Champion 16093; Lew Childre, HORSIE KEEP YOUR TAIL UP; recorded 9/11/30.

Conqueror 8656; Lew Childress, HORSIE KEEP YOUR TAIL UP; recorded 03/24/36.

Decca 2511A; Freddie Fisher & His Orch; HORSIE, KEEP YOUR TAIL UP; recorded 4/11/39.

Columbia 20452; Light Crust Doughboys; HORSIE KEEP YOUR TAIL UP; recorded 11/6/39; composers: Daly & van Ness

Vocalion 5227; (same as Columbia 20452).