Maybe not what you're thinking - it has nothing to do with the rumor that she had relations with a horse, but I was told that CtG rode an Appaloosa. She is depicted in a painting in a men's coat riding astride on a horse that could be either a fleabitten grey, or a leopard Appaloosa.
I have been trying to do research on the history of Appaloosa horses outside of the Nez Perce and asking a few ladies who are interested in side saddle riding led me to researching Catherine, but I would like to find someone else who might be able to give me some more insight as to whether or not she rode spotted horses, or had an affinity to a certain breed or color of horse at all.
Many Europeans rode spotted horses. It is highly doubtful before the 20th C. that any of them were Appaloosas.
Your research should have told you when the Appaloosa developed after 1750, when the Nez Perce began selective breeding. Naturally, the breed didn't fix overnight. So you have to look at it as a 19th C. breed. There was little trade in Appaloosas, and they nearly died out c. 1880.
All being descended of European spotted horses, we shouldn't be surprised to see not-Appaloosas and pre-Appaloosas in European art. It starts with some spotted wild horses in cave art. They appear in ancient Greek and Han art. Medieval destriers were often spotted (Ayton, Knights and Warhorses, Military Service and the English Aristocracy under Edward III). There was a positive fashion for spotted horses in the mid-1700s, so we find not only Catherine the Great but Louis XIV on spotted mounts. Spotted European breeds include the flea-bitten Knabstrupper and the Noriker or Pinzgau (Silver, Guide to the Horses of the World). These are older than Appaloosas.
This probably contributed to the availability of spotted horses to found the Appaloosa breed. In 1806, the diary of Merriwether Lewis notes that most of the horses of the Nez Perce are solid-coloured, while noting maybe 10% were patterned.
So this claim is a matter of people thinking any horse with a pattern now found among the Appaloosas means the horse must be one, not realizing how relatively recent the breed is.