I've heard a few ways of describing such a fantastical beast, but I don't know which is correct.
They are known as both Alicorns (Ali supposedly from ala (wing) and Corn meaning horn), as well as Pegi(a)corn, a portmanteau of Pegasus and Unicorn (I've seen both an i and an a used).
which of these is most 'correct' and did one come first? Furthermore wikipedia says that
The horn itself [of the unicorn] and the substance it was made of was called alicorn, and it was believed that the horn holds magical and medicinal properties
So that would make my supposed etymology above wrong.