These are colored cobs and vanners doing the job they were bred for. Quite the sight.
Note the slightly smaller and more dished heads on the British horses pulling caravans, whilst the American horses later in the videos are a little larger and draftier - there's a split going on in the breed between the preferred UK type and the preferred US type.
One argument people use for not wearing helmets or putting them on their kids is that good riders don't fall off.
Exhibit.
This little girl did nothing wrong. It wasn't a great run...she went way wide around the second barrel, but hey, she's a kid. She was out of the horse's face and when the horse started to go down, she did what she could to try and rebalance the animal.
According to the videographer, apparently her father, the going around the third barrel was very wet. It's not uncommon for barrel horses to slip like this and it seldom results in significant injury to the horse. (I also had this happen to me when I was a teenager in the jumper ring...with the same result - neither I nor the horse was hurt and we got back up and carried on).
But, this does demonstrate that even a good rider on a well trained horse can and will come off, especially if you're doing something more dangerous like barrels or jumping (I put the two about even in the danger rating of equestrian sports). If you ride, you will fall off. It's inevitable. Adults can do as they choose, but it's irresponsible, in my opinion, not to put a helmet on your child.
This rare British breed may remind American viewers a little of the Saddlebred, but it is older and is not technically a "gaited" breed - it has no extra gaits, but it does move a lot like a Saddlebred.
No, these horses are not sored. A good Hackney foal will trot like this in the pasture. They were bred to pull light carriages and look good doing it. They come in two sizes - the Hackney Horse and the Hackney Pony.
(And, yes, they can be ridden. Hackneys and Hackney crosses often make good jumpers).
I hate it. This video explains better than I can why it's bad.
Rollkur comes about because of an obsession with the set of the head over correct carriage. Correct carriage starts at the other end of the horse. Too many people - in all disciplines - start their work at the wrong end of the horse. Pleasure, both English and western, is another place where this kind of thing is rampant.
If you get correct hindquarter engagement and elevation, the horse's head will naturally "drop" or "fall" into the correct position...for that horse. (It's bad to force a headset other than the one natural for that animal. For example, many stock horses will naturally carry themselves in the level position usually associated with pleasure, while Warmbloods and Thoroughbreds tend to arch the neck upwards more).