For most of the background characters, we don't have enough information, so I won't include them.
Twilight Sparkle - She's a screaming INTJ.
Rainbow Dash - She's a fairly certain ESTP.
Rarity - I'm fairly confident she's an ENFJ. The "n" and "e" parts challenged me. "N" for her fashion ideas. "E" is for her living for the next party despite her fairly solitary seamstress occupation.
Pinkie Pie - ENFP. The "n" part gave me doubts. As she seems driven by whatever random idea is in her head, I assigned her N.
Applejack - INTP. It's hard to tell her E/I, but when she goes to the Grand Galloping Gala with the idea of selling apples, I have to conclude that she can't be an E. She also doesn't, inherently, gather people to her.
Fluttershy - She would appear to be an I?FP. As shyness is about anxiety, and not personality, you really can't use that huge part of her personality to determine MB type. I can't get a good enough feel for whether she is N or S. Her anxiety masks that. As she is not the one coming up with ideas, and far more likely to be pulled along even if she isn't shy about something, I'd call her an ISFP.
Spike - ESTP.