After a making a batch of horchata, I always feel wasteful throwing away all of the uncooked rice. Can it be re-used for another batch, or has it given up its good flavors? If not, are there any other uses for it?
You could switch to a recipe that uses all of the rice, instead of just infusing it. Here is an example: http://norecipes.com/blog/2009/03/30/horchata/ .
Boiling rice before its use in horchata avoids big quantities of sediments. After its unncooked use it can be reimplemented, but since you extracted most of his essence, more ingredients will be need to mantain and complement its flavor, plus to a mandatory boiling: Milk-related*, vanila flavor and coconut can do a good companion. Horchatas in México have many variants with the plus of other ingredients, such as strawberries, pineapple, oat and barley. Since rice pudding is the other alternative for the rice left, you may consider inquiring the many posible styles of rice pudding based on its ingredients and use them in preparing more water, like orange skin escence or powder.
*It can be normal, condensend, evaporated or related Milk, Milky Ice cream or similar ones. Since you are dealing with milky products, Another twist can be made while adding liquid milk candy, coffee and matching liquor (Kahluá, Baileys, etc.), but that's likely less to be considered a horchata, then the alternative ingredients mentioned (strawberries and so on) shoud be ommited unless you find a good way to link them.
You can use it for rice pudding!!
I just made horchata for the first time. It turned out great! The leftover ball of rice/almond goo looked perfect for a baked treat. I added a bit of flour, an egg and some baking powder and mixed it all together. I thought I was making cookies, but the texture was more like a bread dough. So, I buttered a baking sheet and spread the dough out. Turned out great! (I baked it at 325 for fifteen minutes). Now I think I'll spread something over the top and roll it up, or perhaps just cut it like a cookie bar. Anyway, it tastes great and the texture is so yummy!