"There is a horse under me."
Translation:Подо мной лошадь.
This sentence is not natural. Russian is my primary language and we don't say like this. We say: "Я верхом на лошади" or "Я на лошади".
Sorry, I don't know how it may be translated into English correctly. But I'm absolutely sure, that "Подо мной лошадь" – it is kind of roughly, literal and unnatural translation.
There is no difference in the meaning. подо is sometimes used when you have many consinants in the beginning of the next word, so that the pronounciation would't take too much effort.
e.g. под столом - different type of consonants, pronouciation is easy. подо мной - м and н are the consonants of the same type, if you add дб that'll take time and effort. Same for подо льдом - under the ice подо мхом - under the moss