Do you have much experience around a saddle seat training barn? I ask, because most of what you describe is not unusual and when done correctly not in the least bit cruel.
Long-lining a young horse for a short period of time is very common and IS very good for teaching the horse to give to the bit and learn voice commands before introducing a saddle. Most are actually driven as the next step in training, prior to riding, to build additional muscle before introducing a riders weight.
A running martingale with two sets of reins are also standard training equipment. Saddle seat horses are usually only ridden in a double bridle a couple times a week to keep them fresh and responsive to it.
Adding draw reins on top of a running martingale is not normal. (I've never seen that type of set-up used..never). Are you sure that is what you saw? If so, that would be excessive.
Twisted wire snaffle (or a double twisted wire snaffle) also normal and in the proper hands nothing wrong with it. Should not be used roughly. We like the horse to be light and response in the bridle, not hanging on the bit.
Western saddle on a young horse, also normal in a lot of barns...just easier to deal with any young horse shenanigans.
Chain over the nose, normal..just keeps the horses attention on the handler when used correctly. Cracking a whip near a horse to focus it's attention also not unusual. Was the horse plunging around out of control on the end of the line or just alert and on his toes? There is a difference. I am betting the horse was just alert (wide-eyed). It would make no sense to crack a whip near a horse that was truely scared.
Just some things to think about. None of these training practices are cruel or unusual when done properly...just may look unusual if you have never seen them or understand the purpose.
The martingale was like the one pictured, with regular reins through it. The draw reins are seperate. They told me what they were doing while tacking up, and said that the draw reins would help my dressage horse with his head. I just said uh-huh. This trainer is not light handed. A lot of jerking goes on when riding the horses, and when I rode one, she said I wasn't jerking hard enough, while my hand were hurting.
The long lining I for sure know about was being done on a 18 year old mare, that has minor joint problems. They jerk on their mouths while doing that too.
With the halter training, the chain was under the nose, so whenever the chain was yanked HARD, the horse threw it's head up in pain and fear. The whip was making contact, multiple times. At the end of the session, there was lines from the whip down his side. This horse was not "alert", he was terrified. When she was walking back to his stall, I could tell how stressed and fearful he was just by how he was walking. This was by no means "training", this was downright cruelty. I know it happens in other barns, but it was like really? The trainer had 2 stablehands watching and learning that this was right.
At the arab shows I go to, I'm fine with people chasing their horses with plastic bags, because it's not making contact. But whips? Unacceptable