Going on life experience, horse shows generally kick off very early in the morning and go a l l b l o o d y d a y .
My Dad was invited to drive and tow the float, which he did once. He was less than impressed with sitting watching the lack of action all day, so Mum drove from then on and Dad played in the shed. He was more than happy with that arrangement.
Cattle are loaded by just shoving them in until the truck is full. They are quite robust animals which brace against each other and travel reasonably well. If they stomp on each others legs or get a bit bruised, they it isn't a massive issue, they just cut those bits off when they process them anyway.
Horses on the other hand. Their legs are more fragile and have a nasty habit of going down in the float and knocking themselves around, so they have bandages on the legs and 'bell boots' to protect their ankles and feet. People also want to ride them and need the horse to perform well, no one cares if a cow is a bit stiff, only that it is tender.
When they truck them they generally load them in sideways and have boards that run from one side of the truck to the other to hold the horse in place, then another horse, then the board etc. Doggers, they just shove them in.
In floats, some are 3-5 horses in at a 45 degree angle or 2 facing the front.
We had a horse that would tow fine in a float that had a tiny window at the front, but would freak out and fall over on corners in a float with a big front window. I'm guessing that she didn't like seeing the car disappearing from her field of view and would try to corner herself... and fall over. Cover the window in paper and she was fine.