The following events are what I would consider to be the main events of Black Beauty.
I would say that Beauty's birth should be the first main event in any list, as the story would not exist without Beauty's birth. Your list may include anything that you find of importance from Beauty's early life while owned by Farmer Grey.
Next should be Beauty's sale to Squire Gordon at Birtwick Park. Beauty's life here is wonderful more often than not, and he meets a lot of other great horses. The stable fire could make a list of important parts as would Beauty's night ride to fetch the doctor.
Squire Gordon is forced to move to warmer climates and sell Beauty. The next few owners at this point are less than great. Beauty is injured and permanently scarred, and that forces him to no longer be a carriage horse.
Beauty is eventually sold to Jerry, and Beauty is finally once again in the hands of a loving owner. His time with Jerry is short-lived, as Jerry is forced to move to the country and sell Beauty. There, Beauty is worked until he is practically dead, and Ginger does die.
Beauty is bought by a kind farmer and his grandson. Together, they nurse Beauty back to health and eventually sell him to a family that recognizes him as Squire Gordon's prized horse.