The question is what the woods symbolize to the traveler. What has he said "no" to in passing by in "Stopping by Woods on a Snowy Evening"?
In the poem "Stopping By Woods On A Snowy Evening" the poet Robert Frost describes how a winter traveler takes time out to do nothing but gaze. He is transfixed momentarily by the image of white silent stillness. In this particular poem, the emptiness and stillness seem like a positive thing - a thing which beckons through it's peacefulness. It is worth remembering however, that Robert Frost himself had a divided view on solitude - sometimes it could represent the positive (peace) but other times the negative (loneliness). In this poem he decides to move on - perhaps towards a destination and company? He has time however to drink in the beauty of the night, before reality cuts in and reminds him and his horse they have places to be.
I think that, when the traveler passed up stopping in the woods, he is choosing to do what he is supposed to do rather than what he wants to do. If you look at it like that, the woods symbolize his desires -- ones that go against his duty and his obligations.
When the traveler stops, he is trying to go against his obligations and just enjoy some time for himself. It is tempting to do so, but eventually he says "no" and gets back to what he is supposed to be doing.