what are some fun things me and my horse can do when I'm not riding him. like when he's in the pasture? and what are some things me my horse and my friend could do at the barn?

I always enjoyed grooming my horse. You could braid his mane and tail , and the more you brush him, the softer and shinier his coat will be. Make sure his stall is spotless, and spend some time cleaning and polishing your tack. I always liked hand-feeding mine pieces of carrots. It's an easy way to teach them to come when they see you.
If you hang out with him, he may come up with some ideas, just pay attention. Have fun!

decorate stuff for him (saddle pad, trunk, etc)
play games, see if he will come to you,
play hide and seek
put a carrot in your pocket and see if he will follow you