Semantics apart, are there likely to be measurable individual 'personality' differences between horses? Well yes, It does seem as if there are. But these are more likely to be behavioural differences rather than what the horse actually 'thinks'.
Some research has attempted to adapt human psychometrics for horses. But as the horses can't complete the tests themselves, the results may be affected to some extent by the personality of the assessor. In one study, handlers were asked to rate horses according to the Big Five factors. One of the major theories of personality states that all individual differences can be described according to how you score on each of the 'Big 5' traits.
- Openness to Exerience
You can read the results of the study here:
Can Judges Agree on the Personality of Horses?
If you are interested in the human application of these traits, please check out the 'Psychology Articles' page of this blog for some fun interactve articles where you can explore your own personality traits.