Lol. ala - is latin for wing. Corn is latin for horn. - that's where alicorn came from. As for making the term popular in that usage you can blame Piers Anthony.
Dunno about Piers Anthony use of the word, but I remember learning the term "alicorn" as a name for winged unicorns from reading really old (and pretty bad) fantasy books published around the 40s, when fantasy novels were super dry and full of themselves. (It was all our crappy library had till they expanded the building. Don't judge, haha.) No wonder I switched to Terry Pratchett and never looked back.
But I remember being really confused when I later learned "alicorn" as a name for a unicorn's horn since I knew it as a winged unicorn first. "Don't these guys know an alicorn is a winged unicorn?" I think I had much internal rage over that as a child till I learned it was okay for the word to have two meanings.
To Al-1701: it's pretty common for words to change spelling over time, 'specially when they're combined or translated from another language, so maybe that's what happened there?