There are horses of mythology (including flying horses) and also horses of legend, and they are all stories you could retell for your project.
Research Tip: You can zoom in on the horse stories from a particular culture, or you can combine stories from different cultures; your research will depend on which approach you want to take. A good place to start is Wikipedia's list of mythological horses, along with this list of horses in folklore and mythology; there is even a list of winged horses. Starting with those lists, you will find articles on all kinds of horses and horse stories!
Past Projects: