I've heard quite a bit about this show and seen a few episodes, so I'll take a guess.
Twilight Sparkle - ISTJ. She reminds me soooo much of my best friend. Introverted, smart, serious, tidy, dutiful, rule-follower, but easily stressed out and kind of bossy.
Pinkie Pie - ENFP. She could be an ESFP because she's very much a "party person", but has a big imagination and a bit out there.
Applejack - ESTJ. Never neglects chores, does what needs to be done, practical.
Rainbow Dash - ESTP!
Fluttershy - Maybe an ISFP? She's very sweet and gentle.
Rarity - ENFJ. Kind, sophisticated, with a bit of a dramatic flair.