Microscopic examination of the horses eye shows them to have two types of cone cells and so they should have colour vision but perhaps this will be limited in comparison to human colour vision. Which colours horses can detected cannot, however, be established with a microscope. Studies have shown that they can definitely distinguish red to a certain extent but not as clearly as with yellow, green and blue. In the studies, the colours were distinguished from grey and were chosen around 95% of the time so it does show a high level of recognition.
So yes, they do see colour but not in the huge spectrum that we do. And their depth perception is much different to ours but that's a whole different thread lol I've already said more than I needed too lol