If a horse does not longe on a rope out in the open (no fences), it is not trained to longe. Longing in a round-pen or with any fence that becomes the the barrier or perimeter to the horse only teaches it to follow the fence. It is really not trained to longe at all.
We teach a horse to longe out in the open like I did for the 30 or so years that I taught them to longe before I had a round pen. When I started teaching horses to longe, the only round pens that even existed were about 20 feet in diameter and were only used for 1st rides.
Horses only 'pull' on you if you let them. It takes two to tango -- so to speak.
We teach horses to work on a rope with slack in it from the very first time we ask them to move forward around us in a circle. I'll start out with about 8 or 10 feet of line using only a stiff rope halter. They already know that a 'smooch' means to move -- and move now! They have already been taught to move over with a light touch and a smooch. Later, it will only take a smooch and the tinyist bit of body language to have a horse step over for saddling, grooming, etc. They will already know that when I am in front of them and step toward them and smooch, that they are supposed to back up. They will all move either shoulder over or either hip over if I just speak to them and exhibit the body language that tells them where to move.
I teach them that when I hold one hand (with the rope) out in front of them and my other hand raised behind them and smooch, they should move forward. Think of it like a horse standing there with several doors surrounding it. There is a front door, a back door and a door at each hip and shoulder. When a horse has been told to "Stand!" or "Whoa!", all of the doors are closed. The horse is scolded for moving any foot anywhere. This is how we teach horses to stand still when we saddle or mount or doctor them.
When the front door is open -- like when you want a horse to longe forward and indicate so by holding your hand out in front of the horse -- and you smooch, an obedient horse will step forward. I just have to raise by hand that is behind the horse and smooch and any horse I deem 'ready to longe' will step forward. If he pulls or goes faster than I want, I DO NOT say "Whoa!" but I pull hard and pull him around. This will make him stop and face me. Then, I indicate again for him to go forward and smooch. I seldom have to re-start a horse more than 2 or 3 times and he figures out to go slow and to not pull.
When I want to reverse him (which I do frequently), I pull him into a stop, change hands on the line, and he quickly learns to go the other direction. Again, I just raise the hand behind him and smooch to tell him to go.
When he walks obediently, I ask him to jog on the line. The line still will not be over 10 or 12 feet long. When he jogs nicely, stops and reverses nicely on that short rope, I let him out farther and farther until a few days later he is walking and trotting on a 25 foot rope. The only voice commands I use are the 'smooch' to move and to move faster and "Easy" to slow down. I do not use "Whoa" or stop or any other voice commands. When I want one to stop, I pull hard and pull the horse around to face me. After a few of these, a tiny 'tug' on the line will stop a horse. The horse is more than willing to keep a little slack in the line. None of them pull after a few hard 'pull-around' stops. If I say "Easy" and the horse does not slow (like from a jog to a walk), I give a tug and then immediately smooch (to keep him from stopping) and they soon figure out that 'easy' means 'slow down -- now'.
When a horse does this correctly (anywhere from 4 days to a week) it is ready to lope/canter on a loose line out in the open. About all of them just speed up to a lope on a loose line when I smooch at them while they are trotting willingly. A horse will become as obedient and precise as their handler is consistent and demanding.
When I used to seriously train jumping prospects, I could take a horse through a complicated course over 8 or 10 different jumps on a longe line. I could walk or run with a horse and it stayed the exact same distance from me no matter where I was. I would walk forward and they just stayed in perfect relationship to where I was. When I headed one to a jump (some over 5 feet high and 6 to 8 feet wide), they willingly went over them. I never had to use a whip (pretty difficult under these circumstances) and seldom had a run-out or refusal. [They were usually my fault for not heading a horse straight or directly at a ump.] Some of the jumps I used were only 6 to 8 feet wide. I did this only for the sake of obedience. Many of my jumps were completely solid.
I could do the exact same thing with trail obstacles. They would negotiate a narrow bridge, a water filled ditch or anything else I wanted them to carefully but obediently go over or through.
It is all a matter of communicating with a horse in a way horses understand and being 100% consistent. It is a matter of always thinking that a horse is only as well-trained as the worst performance or behavior that you accept. You get lax or sloppy or less demanding and they instantly get sloppy and less responsive and obedient. It is just how it works.