It depends on who is saying it.
Sure, sometimes people use the word to mean 'pretty' or 'attractive'.
In a lot of horsey groups, 'cute' is actually an insult or at least mildly derogatory. It means that the animal is not a good mover, doesn't perform well, etc.
In some groups around here, 'cute' means 'average' or a 'lightweight' (can't perform well). It can be very derogatory, and even reflect on the rider or owner, as in, due to such limited ability, the rider only needs something that's limited - 'that's a cute horse for you'.
Or it can mean, 'has a nice head, ears, color or a nice tail, but that's all'.
A 'cute little mover' is a horse that can't trot his way out of a paper bag even with help. A 'cute jumper' is one that performs in the easiest classes and has no scope.
I think it originally came from show hunter people, I think I've even read George Morris use the term.
But I've also read him refer to a horse as a 'tasty jumper'.
There is a point beyond which, one should not go, in making up one's own slang, and then disseminating it through the horse world.
At some point, it actually was a kind of 'horseman's hyperbole'...instead of saying fantastic, out of this world, shrug diffidently, act very casual and cool, and say, 'welll....yes...it's a good horse...'...in other words, the typical tack of a horseman who is making sure if he ever wants to make an offer on the horse, everyone will think it's at least a little bit closer to worthless.
And of course, the REAL trick of it is that some people mean praise with the world....and some don't, LOL.
