What are the best foods to eat while astride a horse?

Eat an ice cream cone and see how neat it is riding a horse while eating the ice cream cone.

Forget the food, just drink alcohol. It'll make your horse seem like he's the best horse in the world after a few shots in.

Don't understand why you need to eat while mounted on a horse.  But if you are referring to snacks, then try attaching a cloth bag to your saddle where you can easily reach it. You can carry crackers, and all sorts of buts, candies, and and apple or oranges.

Cowboys carry jerky to chew on while riding. 

We usually didn’t eat while on horseback but we did go through several drive through getting our lunch and dinner.  Usually tacos and subs. 

Good finger food are the boneless chicken and those little hot dogs, anything fancier and you would need more than a napkin to put it on.

We always had carrots, cucumber slices and grapes to snack on when doing long trails.  We did picnics which usually consisted of grilling dogs, brats and occasionally burgers if enough of us got together.

Type of horse shouldn’t make a difference, a well trained quiet mount that trusts you is important.  You couldn’t eat safely on a Nervous or skittish mount.  And skittish horses won’t tie well during a picnic.   

When we ate we usually had a flake of hay or some grain for our mounts, depending on hoe long we were out and how far we went.  Our trails usually ran 25 to 50 miles of hills, lakes, creeks and a few tie stations.  There was always fresh water available for the horses.

I suggest finger foods for ease of consumption.    I also suggest some foods the horse can eat, so you can reward him for standing still and letting you eat.

Maybe  a sandwich, like sardines with alfalfa sprouts on whole wheat bread.  I've known horses who liked sardines, and never known one who disliked alfalfa.

For appetizers...  carrot/raisin salad, apple fondue, soldiers on horseback,  oat crackers with pesto, etc.

tacos

(the real ones, not those horrible soft tacos)

spaghetti and meatballs

There's an Italian cheese called Cacciacavallo that's shaped so it hangs over the saddle,

It's actually not a great idea to eat while riding.  Not the best way to digest.