He's an INTJ written by an INFP.
I've always identified with him very strongly.
Whoever said his spells didn't have a purpose obviously didn't understand the environment Snape grew up in. Muffliato, great for making sure you aren't heard. Sectumsempra, something to really hurt the other person fighting you. Various potion changes, made to increase their efficacy and efficiency. Learning how to fly without a broom, pretty handy when you need to fly and don't have a broom.
Another clue that he uses Ni fairly regularly is his tendency to quickly draw conclusions. It's Ni pattern recognition. A Ne user would not be so quick to draw a conclusion.
He sees things from his own perspective and isn't really interested in anyone else's.
I actually see him more as a type 4w5 INTJ.
suicidal despairSome 4/5s place little attention on appearance, beyond a kind of casual style. Black clothing is common, loosely worn and maybe not very well-fitted. By contrast, there are other 4/5s who are careful to dress well whenever possible. Well-dressed 4/5s seem to have a way of looking elegant but understated. Whether or not they dress and groom themselves carefully, average to unbalanced 4/5s often feel they are unattractive in some way.Unbalanced 4/5 can move into the extreme withdrawal of depression, then, with still further disintegration, into a sort of dark impulsiveness. Deeply troubled by feelings of utter worthlessness and extreme isolation, unhealthy 4/5 may look for opportunities to perform degrading, menial tasks, rationalizing that such a fate is deserved. Servility and self-abasement provide a kind of barely-adequate, very temporary relief from the constant torment of self-hatred.
As life becomes less and less tolerable, suicide becomes increasingly likely, and if it happens it may be done in some unusually gruesome way. Extremely dark, horrifying inner imaginings are welcomed and encouraged. The whole world, both inner and outer, is seen as grotesquely diseased and utterly without redeeming qualities. 4/5 Hell is a place of unimaginable ugliness, populated by those deformed, psychotic monsters, the human race. Psychotic 4/5 revels in hopelessness and despair.