I'm sure there are dominant traits involved to some degree. Most likely determining their body structure (bone/muscle density and whether they have wings or a horn), and the capabilities of their magic. I would also say that a lot of, if not most, ponies are hybrids between the races to some degree. Given that the population has been intermingling for over a millennium.



The main exceptions would be the populations of Cloudsdale and Canterlot. With both having high pegasus and unicorn populations respectively, and most likely to have less hybrids due to that. However, it's hard to say just what the ratio between races would be since we've only seen only small samples of Equestria's population.