The night started with the star sharing the best actress prize with Glenn Close at the Critics' Choice Awards.
But she wrote on Twitter: "Just after the show I learned that my dear angel of a horse, Arabella, is dying.
"I am rushing to her now to say goodbye."
Goodbye, my angel ? pic.twitter.com/KnWlt2ryuC— Lady Gaga (@ladygaga) January 14, 2019