Cloudy sake...that's my favorite stuff, called nigori sake. Usually sweeter and milder in taste, although it can be plenty strong in ABV, still. Nigorizake is what I pick up if I'm going to watch Toshiro Mifune movies! Nigori sake, yakitori, and one of those long, black and white Kurosawa period piece movies makes for a nice evening.
Horchata I don't think would actually ferment properly, at least in a sake sort of way...I made the suggestion in jest...the sake fermentation process is actually a lot more complicated, not though I could adequately explain it, but it involves the use of something like a benign mold to convert the starches to a fermentable status. Now, horchata is probably sweetened with sugar, so THAT would ferment I bet, and you would then have a very low ABV thick rice beverage, but I doubt the rice would be converted to alcohol in the way sake does.
But nigorizake is great. If I wasn't so cheap I'd have it more often. Not that its that expensive, I guess, but I barely buy commercial beer any more, such is the expanding extent of my cheapness. Someday I'll start trying to brew it meself.