If you want to keep your characters consistent, you need to understand who they are, and how their various personality types will clash or mesh with the other characters'. Snake being very, very different from the mane six, plotting out how their characters would interact and getting it down on paper (so to speak) is a very, very good idea.
So I wrote this out to consult, and decided to post it publicly, rather than hoard it to myself. You're welcome.
Solid Snake and...
Twilight Sparkle: Twilight is nominally the leader of the mane six, so Snake generally defers to her when it comes to the order of battle. At the same time, he frowns upon what he perceives as Twilight putting Spike in danger. You guys might have noticed, but Zanzibar Land is sort of a running theme in this story, and I like to think that what Snake saw during his mission there, specifically with the children Big Boss intended to train as soldiers, left him with a deep-seated contempt for child soldiers, or for putting children in danger (not to mention his history with Frank Jaeger and Raiden). He doesn't fathom why Twilight would allow Spike to follow them as far as she did.
For Twilight's part, she swings between exasperation and fascination regarding Snake. He's exotic, being from another world and all, and his actions and motives remain enigmatic; she can't quite figure him out, but she'd very much like to. But they butt heads often enough to form a bit of resentment between the two of them. She chafes under his occasionally patronizing and hard-nosed approach to interacting with the others. The more time they spend one-on-one, the more conflict will crop up between them.
Pinkie Pie: Snake is disturbed by Pinkie, and his inability to comprehend her antics makes him avoid her, or thinking about her, whenever he can.
Pinkie views befriending Snake as both a challenge and a game. She wants to get to know him the same way she'd want to get to know any new friend.
Applejack: Snake and Applejack initially didn't get along, but as time progressed, Snake began to see her as the most capable and dependable of the group. She's the only one he gets along with, and consequently, the only one he'll consistently address as an equal.
Applejack harbors a debt of gratitude to Snake for his efforts in rescuing and defending her sister. She believes that he'll do the right thing, even if it takes a little prodding, and will always try to appeal to his better nature.
Rarity: There's a bit of camaraderie between Rarity and Snake. She thinks of him as rakish, and a bit of a ruffian, but grants him a great deal of trust, especially after the events in the Everfree Forest.
Snake, for his part, doesn't dislike Rarity, though her habit of putting on airs gets on his nerves.
Fluttershy: While frustrated with Fluttershy's presence on the team, seeing her as dead weight and not much else, Snake doesn't raise a fuss over it, knowing that Twilight wouldn't think of sending her away. After the fight with the timberwolves, Snake saw that there was more to her than he'd initially thought, but he wouldn't trust her with his life.
Fluttershy instinctively wants to understand Snake, but is too intimidated by his rough exterior to approach him.
Rainbow Dash: Mutual animosity. Snake sees Rainbow Dash as arrogant and headstrong, and Rainbow Dash is continually put off by Snake's casual patronizing of her friends. She feels that he underestimates them while overestimating himself, and doesn't trust him to stick by the group when the going gets tough. With her athleticism and Snake's sheer combat ability, the two could form a potent duo if they could ever get past their personality conflicts.
Applebloom: They have something of a big brother/little sister relationship, antagonizing each other to hide their affection. Applebloom views Snake with a sort of childlike wonder. Snake feels protective of Applebloom; her youth and innocence are what drove him to rescue her from the manticore, and he takes personal responsibility for Trenton's capture of her.
Spike: No affection whatsoever. Spike sees Snake as a grown-up who underestimates him, and Snake sees Spike as a little kid who will make grievous mistakes in a misguided attempt to prove himself.
Big Macintosh: Their first meeting involved Snake shooting him (albeit non-lethally), so I can't imagine there'd be any love lost between the two of them.