My name is Pat Davitt. I assume from your post that someone else is transporting your horses to the shows. Down here in Texas when someone says that they have "many, many dogs"; that normally means 10 to 20. Not sure what "many, many dogs" means in Missouri.
Or, how large they are. The reason I ask is that, if you have more than 4 dogs, you may want to consider a "Toy Hauler" trailer (5th Wheel or regular). You can turn the garage area into a dog area instead of using it for ATVs, Motorcycles, etc. I have a friend who shows dogs, and that's what they use.
Not trying to turn you off on Airstream, but I am a practical person. Any travel trailer is designed primarily for humans, not for large numbers of animals.