I think there are as many horse personalities as there are people personalities.
I always saw it like this- your personality is the result of many, many things, including your genetics, childhood atmosphere/ environment, etc. I can't say I believe in astrology, but everything I've read about my sign (Taurus) has lined up perfectly with everything I know about myself- so, I haven't rejected the possibility of there being other factors in what makes a personality.
I don't believe that personalities, for horses or people, can be broken down into four categories, or whatever number someone's trying to sell at the moment. Everyone tries to do that, but in the end they always end up adding that 'and all the other stuff that doesn't fit here or there' category. It's like trying to sort millions of marbles into X amount of boxes- do you sort by color, pattern, size...? What if you have a marble that's swirly, but is also blue? Does it go into the blue box or the swirly box? You can ignore one or the other, but the marble is still both... and then you still only have so many boxes.
To me, those '4 types of horse personalities' things are just very general guide lines- you can pick the one that fits your horse most, and try to use those methods that it prescribes. But in the end, I don't think it's something to put a lot of faith in at all. In all my experience with horses, I have never once needed to look up a guide to personalities in order to find out what the horse is- the best possible way to do that is to observe and work with the horse yourself and form your own conclusions. You don't need someone else's observations of other horses to tell you what your horse is in your eyes. Same with people. You can tell me a person is a Sagittarius, a Type A personality, whatever, but it means nothing compared to my observations which can tell me if that person is shy, nice, easily offended, emotional, etc. Of course, this is coming from someone who's very good at reading other people and especially animals...