What is the name of the first horse breed?

most people think it is Arabian but it is a mustang not Arabian

The most ancient breed of horse (still in existence) is the Przeswalski's Horse.

The Arabian along with the Barb, Turk and Akal Teke are (arguably) thought to be the main, ancient light horse breeds used to produce all modern non-draft breeds.

The mustang is a feral horse decended from Spanish horses which were produced

using the above breeds and stock native to Europe. The US government and also

some ranchers "improved" the mustang in many areas by turning out remount stallions (generally TBs or Stockhorses) in an attempt to produce larger horses for the US cavalry with the endurance and thriftiness of the mustang.