I wonder if they’d have different sites of higher education for the different types of ponies … because there are different skill-sets there — dealing with flight and weather conditions, or building/planting/growing stuff, or using magic. Or would there be some social-engineery type who would point out that separating the pony races for education was harmful, and perhaps impose some sort of [George Reavis's] The Animal School model, where all Pegasi were required to at least attempt both magic and gardening, and all Earth ponies were required to try flying? (I can see the lawsuits coming.) Of course, if it was like typical American universities, rather than lower-level schools, there would be different “majors” for different skill sets. (Hrm. Kind of like our aviation school, and the more applied of the sciences programs, and … I don’t know what would map best with Unicorn Magic as a major. Art and Theater, maybe?)
I don’t think that there’s a whole lot of segregation in Equestria, except to the extent that it’s a function of actual physical differences. Everypony in Cloudsdale is, of necessity, a pegasus; the only way a unicorn or an earth pony is setting hoof in that town is by means of a temporary spell. There exists a string of mountains called the Unicorn Range to the south and west of Cloudsdale, and unicorns are apparently dominant in Canterlot, but there’s no physical limitation involved: pegasi can certainly fly to these heights, assuming adequate wing power, and earth ponies can walk or take the train.
Educational opportunities, I infer, work the same way. Princess Celestia’s magical protégée of necessity would be a unicorn (Twilight Sparkle). Musical talent, however, may be distributed among the tribes: stringed-instrument specialist Lyra Heartstrings is a unicorn, but cellist Octavia appears with two different quartets in two different episodes, all comprised of earth ponies, and Scootaloo, a pegasus filly, apparently can play the piano.