Absolutely not, it's an urban myth.
Catherine died in bed of illness; there were no equines involved and a Catherine/horse nexus was never attempted.
Catherine the Great of Russia's death while attempting an unusual practice with a horse is one of the most virulent myths in modern history, transmitted by whispers in school playgrounds and lecture halls across the western world. It's unfortunate that one of history's most powerful and interesting women is known to most people as a beastite, but the combination of perverse rudeness and the relative foreignness of its subject makes this a perfect slander.
So if Catherine didn't die while attempting sex with a horse (and just to reiterate, she absolutely, 100% didn't), how did the myth arise? During past centuries the easiest way for people to offend and verbally attack their female enemies was sex. Marie Antoinette, the hated queen of France, was subjected to printed myths so deviant and obscene they would make spam emailers blush and certainly can't be reproduced here. Catherine the Great was always going to attract rumours about her sex life, but her voracious sexual appetite – while modest by modern standards - meant that the rumours had to be even wilder. Historians believe the horse myth originated in France, among the French upper classes, soon after Catherine's death as a way to mar her legend.