That video was cuts from different days out, it isn't always like that and varies a lot even within each Hunt as to where they are meeting. Some days you can get stuck in woodland or forestry and it is totally different
As for clothing, hunting gear is exceedingly well designed. Hunting capsto protect ones head, although way back it was top or bowler hats for the field and only Hunt staff wore the actual caps.
A stock, properly tied, not these pre tied things, supports the neck and can act as a bandage or a sling.
A hunting vest, made with a wool mix, is warm and has no collar so the stock can be fixed to it.
A waistcoat, added warmth.
A Hunting coat is a wool mix, it is thick and heavy. Practically waterproof, it is warm and also acts as a good protector in a fall.
Breeches, most wear the modern ones as they are easier to wash and the thicker variety are warm.
Boots, Hunt boots are made from box leather, this is when the inside of the leather is on the outside. This is so that when they get scratched working over the surface with a deer bone, removes all the scratches and working on them with polish and a bone, you can bring a polish to them as bright as patent leather.
This is called boning and a dying art.
Fox Hunting was changed in 2004 when effectively it was banned. As with many Acts of Parliament, it was very badly written and all Hunts continue within the law. It is a bit like a Drag Hunt in that someone lays a trail but chances are a fox will cross that trail and Hounds will veer onto that scent.
As for jumping, again it varies greatly. Fields are a lot smaller here, especially grazing fields, so there are plenty of hedges, a good stock proof hedge will have no wire in it. Hunts build jumps, with the farmer's permission, if there is wire.
I can assure you, when Hounds are running and your horse's blood is up, you take on fences that when you walk and see them, you think you are insane to have jumped it!