Do not drink anything. Although if you are sweating much, that won't be a problem as far as going to bathroom. And don't worry about another buddy to drag along, either horse or rider.
Make sure you go to bathroom before you go, and then just ride out. When he balks, just make sure he is facing in way YOU want to go. And just sit.
Nothing more. Just...SIT THERE. No battling, no trying to move his feet, no trying to urge him forwards. Just sit there, facing the way he wants to go. If he begins to back, circle him to the correct direction, and then sit.
Don't fight with him, not any. As long as he is facing the way you want to ride? Just sit there.
IF he moves a foot in right direction, let him go, NO PRAISING AND NO PATTING!!!! In fact, don't even make it apparent that you have noticed he is moving, other than to let him move, but only in the correct direction.
And NO TALKING to him at all! Silence.
Be prepared for this to take a while, some horses are much more stubborn than others, others will ride out fairly quickly, once they realize there is nothing to battle against. Once horse thinks it is your idea to stand around? Many times it ceases to be such fun.
And the NO battling, talking, or fighting with horse? Makes horse think you really don't care whether you sit there all day or not. And horse then decides moving off in correct direction makes sense, since it isn't YOUR idea.
As long as horse is moving in right direction, let him do so. If he turns to barn, or begins backing? Halt him, turn to the direction you want to go in, and go back to sitting.
Do stay alert though, and wear a hat and sunscreen.
Also, and this is only if you can mount easily, take a little bit of grain, and feed him away from barn. And I don't mean within sight of barn either, but away from it. Those days don't grain at barn.
Again, the key to this is NO praising, NO petting, and NO fighting with horse.
As to round penning, you can do it also if you have good corner of fencing, that gives you two sides, and you can just hold lunge line and keep horse in circle, IF horse respects you. For this? I would not just use a halter but rather have a headstall set up with smooth snaffle, and use lines made out of the soft rope, about diameter of pencil, that you can burn ends to melt?
Take a swivel snap, not a large one, and run it through the ring on swivel snap, and the fold back, with needle and thread, (good quilting thread) sew through the two pieces, and whip around it too, so rope is sewed to itself, and then bind around that with black electrical tape. Needs to be 25 feet long.
With headstall on, from the side you will be facing as lunge, run swivel snap through the bit ring, over poll and down to other ring. Will have to swap it when horse is going other direction. This gives you more control than a halter does.
Horses make me a better person.