Talk:The Crystalling - Part 1/@comment-27214641-20160326163603/@comment-26356822-20160326191111

"Alicorns are pony characters in the show and other material who have both a unicorn horn and Pegasus wings and, depending on the depiction, also have Earth pony power. They are styled as royalty." ~  http://mlp.wikia.com/wiki/Alicorns

So I'm guessing that they have Earth pony power when it's convenient to the plot.