Here’s what “backstory” I have for these two, which I probably will change a bit
 
The Bicorn (I guess is what he’s called, there’s got to be something else because that sounds stupid) is a powerful pony from long ago who wanted to rule equestria (i haven’t really worked out much of his backstory yet) but he lived in a frozen land in the north, he was eventually sealed away in ice, not sure by who yet, but he is later freed in the present by the bat pony
 
The other one is bat pony who was once served Luna, he becomes jealous of the princess’s power, he wants to overthrow her and rule the night. He learns of the Bicorn from long ago who is still frozen in ice, he frees him and tells him he will help him take over equestria, and recruit some others to help as long as he can rule the night.
 
The versions of these characters in Equestria Girls are in an anime club and are just huge nerds, they aren’t very popular.