Yes, so in general horses that fly are very expensive horses, like half a million or more. They tend to have their own personal grooms who often are tasked with flying with them. If not then there are flight grooms who work exclusively on horse transport flights. I haven't read into the details of this incident but I suspect that there was more going on. There is no reason why they couldn't just catch and return the horse to the stall. Seeing they asked for a vet I would say the horse was injured in a way that made it an emergency.

Fun fact the grooms will feed the horses carrots on takeoff and landing to help get their ears to pop.

Cargo 747 pilot here! I've flown horses a few times and yes, we have extra crew on board to take care of the horses. The handlers ride in some extra seats we have on the upper deck and check in on the animals every couple hours to make sure they have food and water. I've been told that most of the time the horses are fairly well trained and are calm during the flights but every once in a while they get unhappy and bite the handlers. I haven't had any incidents on my flights that I've carried them though.

Ziggurat is correct. The flight ABD4592 was a cargo B747 (registration TF-AMM)

I can’t find cabin pictures but those cargo are loaded with huge pallets, for live animals it’s the same type but adapted, kind of a big metal box but equipped with a door, probably a window and some food/water. At least one human is supervising the cabin but it could be more according to regulations (if it’s the same as for pax) or simply how much the client is willing to pay ?

So the pilots knew it via the aircraft intercom. There’s no chance they would have heard the horse in a 30 years old 747 nor feel any change of center of gravity, specifically on autopilot at cruise level.

Fun fact, the company is bragging about being the Iron Maiden or Olympic flame carrier