My guesses:

1) Clydesdales- I got to pet them at the Missouri State Fair
2) Saddlebreds & Quarter Horses
3) A coggins test is when they screen the blood for the nasty virus called " Equine Infectious Anemia". All horses traveling through other states, and for events must have a coggins test done.
4) If I remember correctly a Thoroughbred and Quarter Horse makes an Appendix Quarter Horse.

I'll leave some questions open for others.