Wow. Now that's a great culture and language question! I've never heard "Russian race horse". Usually it's just "I have to pee like a race horse". People say it when they really have to pee (小便）。 The saying comes from the fact that when a horse pees, a LOT comes out. So people use it to emphasize how much they need to pee. Also, before races, racehorses are sometimes given a medication (a diuretic 利尿剂) that makes them urinate more to lower their blood pressure. So racehorses are often seen peeing. I think most people say this to be funny. You should know that this is not a very polite thing to say, so should only be used with good friends. I also don't think I have ever heard a woman say this, only men. 哈哈。 I didn't think I'd be writing about 小便 on italki!

Very funny!

I have never heard of it.

means, fast