I'm neither Osiris nor Si-amun, but what I could find was the following:
The Arab horse is one of the oldest traditional breeds, its influence shows through in virtually every second traditional breed. The Arab horse’s ancestors, setting off from Central Asia in ancient times, spread to Mesopotamia, ancient Egypt, and the Arabian peninsula as far as the Pyrenees.
I was actually recently looking through some of the tribute that Thutmosis III collected and the spoils of war that he took home.
They often include horses from the North. For example:
Tribute of Retenu (Year 24)
The daughter of a chief and 30 slaves belonging to her, 65 male and female slaves, 103 horses, 5 chariots wrought with gold, 5 chariots wrought with electrum
In year 30 he collected 30 more horses.
Year 30 188 horses (Kadesh)
So quite a few horses came from the north and it looks as though some of their handlers may have been captured as well.
Hope this is what you were looking for