I just found this gem of a handout by the Virgiana 4-H extension. There’s some good horse parts game ideas AND a puzzle already drawn for you, all you need to do is print it! I imagine hiding the pieces around the arena and having the rider find them then put the puzzle together on a barrel.
Note: This is not professional advice, this is a blog. I am not liable for what you do with or how you use this information. The activities explained in this blog may not be fit for every rider, riding instructor, or riding center depending on their current condition and resources. Use your best personal judgement!