I don't believe in such a thing as a horse who is just flat out mean on its own for the hell of it. A lot of horses I've had presented to me as "snotty" or "nasty" or "mean" turned out to love me because I didn't treat them that way and gave them some credit and trust.
I do believe horses can do "mean" things though, at least from a human's perspective anyway. We see them be "mean" to other horses all the time, so why wouldn't they be the same to a human? They aren't doing it to spite anyone, though, purely just to feel powerful. Horses are power hungry.
Also to mention, I've met many clever horses who tried to intentionally rub me off of their backs or ram me into a fence if I asked them to do something they didn't want to do. But then again they might think I'm mean for making them do those things....oh well.
My mare was infamous for biting, kicking, bucking, bolting, ramming people over, shoving people around, pinning her ears and scoffing at everyone, etc. before I had her. Mostly kicking, though, that was the main thing. Just because, not really provoked most of the time. Everyone talked about how bad and nasty she was and were extremely cautious about her. I started working with her and treated her like any other horse and loved on her like crazy and bit back when she would come at me or threaten me. Within a week there was not a sign, and she hasn't offered to bite or kick me in months. She offers me her belly for a scratch and I sit underneath her to scratch it without a second thought. She comes right up to me and nuzzles me and rests her head on my shoulder and dozes. Nasty, awful thing.