I wish more Mexican restaurants served horchata. I've only had it served once, at a hip little joint in the ass end of
nowhere ... specifically, Jackson, TN.
In Central America, it's made with nuts, not rice; I'm not sure if tiger nuts were the original version or not.
Apparently, it's been around since long before Westerners got into almond milk, rice milk, oat milk, etc. Southeast Amerindians made something similar from hickory nuts, broken up, boiled with the shells, and filtered -- I've never tried it. Be interesting if someone tried to commercialize it.
Part of the reason I'm interested is these 'milks' are all emulsions of oils in water, and I had read that Amerindians didn't have any vegetable oils to cook with, and of course no butter -- they mostly used bear fat. But I have to wonder ... it's damned hard to get much accurate info on such things.
ETA: If you're going to go with rice but don't have a powerful blender, there is such a thing as rice flour (used for making very smooth puddings and similar treats), available in most groceries that specialize in Asian foods. Not as cheap as whole rice, but you can find a good deal if you're lucky.