In general the extraverted functions make a person happy.
Is that really how it is, though? The way I see it, you can be an introvert and still be outgoing, expressive and upbeat. I think that introverts get a pretty negative rep. We're seen as the people sitting by ourselves in the corner, fingering a pen or pencil thoughtfully - and that's going easy on us. At worst, we're seen as reclusive, hermit-like creatures that can't socialize and bury ourselves in masochistic loneliness. Haha. Alright, I have to laugh at that image.
It's true that extroverts get assigned positive qualities such as upbeat, outgoing, talkative, expressive, interested (and interesting), funny, laughing, smiling... I think those traits are associated with happiness for a few reasons. One, if you're expressive and feel pretty comfortable putting yourself out there, you must be pretty confident. Secondly, it feels good to express oneself - much better than keeping things inside. But introverts are just as capable of confidence and self-expression.
I think it's true, in MBTI-speak, that extroverts get more energy from the outer world. Therefore, they may appear more talkative and more outgoing with people - and they are. It's because people give them energy, right? The outer world is their oyster. But there's nothing to say that the inner world of introverts isn't just as fulfilling an oyster as extroverts' outer world, is there? Similarly, there's nothing to say that extroverts can't be self-conscious and masochistic, etc.
Introverts do draw satisfaction from their own powers of deduction. Introverts probably enjoy tinkering with an idea as much as extroverts enjoy tinkering with the outer world of ideas and objects. Truthfully, I'm not sure exactly what extroverts think about or are drawn to, but I know that as an introvert, I am just as capable of happiness as an extrovert. Even if I'm not, I refuse to believe extroverts have much of a head start on me, because I don't feel like feeling sorry for myself, haha.
In response to the way you defined extroverted and introverted functions, I'll define the E functions from my POV:
-Fe can make you self-conscious of what other people think.
-Ne can make it hard to sit down and really write a solid, cohesive paper, because you have so many ideas bouncing around in your head. They can overwhelm you and confuse you.
-Te can lead to anger when not everything fits into a neat, defined category. Te can lead to annoyance when things aren't congruent.
-Se can make you hyper-aware of danger in your environment, leading to anxiety. Se may also make you binge eat or overindulge in physical pleasures.
I don't think all the functions are defined well enough, especially the introverted ones, but I think the introverted functions can bring happiness too. Introverted feeling, for example, is capable of placing a pair of rose-colored glasses over your eyes. Those glasses can make you see the world in the most moving and meaningful ways.