What prompted Winnie to venture into the woods for the first time?

The prologue to Tuck Everlasting introduces the reader to Winnie Foster with a single sentence.  

At noontime, Winnie Foster, whose family owned the Treegap wood, lost her patience at last and decided to think about running away.

Immediately, a reader should ask himself/herself "why does this girl want to run away?"  The author doesn't answer that question right away either, which heightens the suspense.  It's not until chapter 3 that Winnie Foster appears again.  In addition to Winnie, chapter 3 introduces the reader to her parents.  Winnie's parents are the reason that Winnie is thinking about running away into the woods.  

Her parents are the quintessential hovering, "helicopter" parents.  They micromanage everything that Winnie does.  

"But, as it is, there's only me. I'm tired of being looked at all the time. I want to be by myself for a change. . . It'd be better if I could be like you, out in the open and making up my own mind. Do you know they've hardly ever let me out of this yard all by myself? I'll never be able to do anything important if I stay in here like this. I expect I'd better run away."

Winnie does not run away right then.  Instead she returns to her house; however, that night she and her grandmother hear a strange musical sound coming from the woods.  By the next morning, Winnie has talked herself out of running away.  

"Where would I go, anyway?" she asked herself. "There's nowhere else I really want to be."

Winnie then becomes angry at herself for not being brave enough to follow through on her decision.  She desperately wants some freedom and independence from her parents, but she can't quite muster the courage to go anywhere.  Then Winnie decides that perhaps she could do a sort of half run away.  

Well, anyway, she could at least slip out, right now, she decided, and go into the wood. To see if she could discover what had really made the music the night before. That would be something, anyway. She did not allow herself to consider the idea that making a difference in the world might require a bolder venture. She merely told herself consolingly, "Of course, while I'm in the wood, if I decide never to come back, well then, that will be that."

What prompted Winnie to venture out into the woods the first time can't be pinned on a single thing.  It's a combination of how she feels about her family, the music she heard, and her attempt to take that first step toward gaining independence from her family.  The woods happened to be close to their house, so they were immediately accessible for Winnie to take her first small steps toward independence.