I would not recommend using uship, but there isn't much in common between dog and horse shipping companies.
Too, when a horse is shipped cross country, there are always delays. It ALWAYS takes longer than the time/mileage in a car would be. ALWAYS.
Extra time is needed for dropping other horses in the load at each of their destinations, for resting the horses, for feeding and watering, and for picking up horses.
The shipper always tries to have a full load on the outbound and return trip.
Trips are always combined unless you pay extra for a direct trip/empty rig except your horse. But that is fairly expensive, and most people do not go to that expense.
A good many people PREFER the 'full load' trip, for several reasons. Horses shipped alone tend to fret and become nervous. When there is a full load, there are periodic stops to load and unload, so many people feel their horses get checked over more frequently, and get to rest their legs more often, and get watered and fed more often. Many people feel horses eat and drink more when other horses are around - the companionship often relaxes horses and they feel more content and drink and eat more.
Even so, horses tend to lose weight on cross country trips. Even so, I do not ever ask shippers to grain a horse during a long trip. Their digestion will go far better if all they do is eat hay and drink water. Constantly eating hay can provide more calories than the grain the horse does without.
I've even had a shipper tell me he has stopped to re-arrange the horses so each was next to one he wasn't tussling with. Though the partitions and how the horses are loaded prevents much of the nipping and tussling reaching a victim, he wanted them all to ride quietly and not get worked up. Kinda nice.
By the way, opinions vary a lot on how to ship horses- bare legged or bandaged or booted.
Generally, western riders tend to prefer shipping bare legged, and there's more of a tradition among english style riders to cover the legs. However, most people who do cover the legs, use the high quality, stiffer, thicker more protective shipping boots, which cover the hocks, heels and coronets, and afford a lot of protection.
The boots should, however, fit very well and not sag or slip, or they will cause more trouble than they'll solve.
Some shippers prefer the horses go bare legged so they don't have to redo the bandages each day, don't have to remedy a slipped bandage or boot, and don't run into possible disagreements with the owner as to how to wrap or place the boots (you know how horse people are).
IF you ship bare legged, you can still put bell boots on all 4 feet - that's really the area that most needs protection in most cases - the coronary bands and tops of the heels.
After a long trip, I generally take the horse's temp morning and night to be sure they haven't picked up a bug from any of the other horses or stables they have rested at. I usually put them into light work immediately when they arrive - light work helps to loosen them up if they're a little stiff from traveling.