The poet stops, not only to appreciate the beauty of the snowfall, but to contemplate life, responsibility, duty and death.  It is unusual for a man to stop in a section of the woods that is remote to observe the beauty of nature, but on this particular night, the poet is thinking about the futility of life.

All this work the I have to do, "miles to go before I sleep," (Frost) wouldn't it be lovely to just lie down in this deep dark woods and rest.  The poet is thinking about death, about how difficult life is, he is tempted by the serenity that the dark woods represents, the snow acting like a blanket to keep him warm. 

On any other night, these same dark woods would be frightening and threatening, holding potential harm for the poet.  But on this night, he finds it fascinating to consider their beauty like a creature of the wild.  In contrast, the horse is impatient to continue the journey, realizing that they have stopped at the wrong spot.  The horse is looking for the barn, for shelter, for rest, but in the right place, the poet, or the man, is considering laying down in the midst of nature, unprotected.

He is hypnotized by the possibility of just stopping what he is doing and allowing himself to become one with nature.  But, the last two lines of the poem indicate that the poet realizes that his duty, responsibility or promises are more important at the moment than his desire for rest. 

The woods are "lovely," but also "dark and deep." This darkness, which seems to exert a powerful attraction on the poet, takes on a vaguely ominous tone in the light of the final line, "And miles to go before I sleep." The two concepts "darkness" and "sleep" can easily signify not only sleep in the concrete sense but also the darkness of death, in whose "deep" the poet could hide from the responsibilities of life, the "promises" he must "keep." We might thus see the poet as being temporarily spellbound by the seductive darkness under the trees, representing a release from human tasks and burdens, to which he only recalls himself by an effort of will.

The deep silence is what also holds the poet spellbound - "The only other sound's the sweep, / Of easy wind and downy flake."  There is a special silence that deep snow brings with it because it acts as a cushion.  Sounds are muffled when there is snow, especially if the snow is gently falling as the words "downy flake" indicate.  This means that the flakes are the slow-falling, fluffy, kind of snowflake.  It is as much the silence as the visual beauty that makes the rider stop.

What attracts the speaker to the woods in "Stopping by Woods on a Snowy Evening"?

Among the qualities about Robert Frost's woods that attract the speaker in "Stopping by Woods on a Snowy Evening" are the snow, darkness, isolation, emptiness, and near silence. Although these may seem like negative qualities, they appeal to the speaker for the temporary respite they offer in the "lovely" woods, apparently in contrast to the village that may be the speaker's point of departure or destination.

The snow is attractive because of its contrast with the dark, and the speaker enjoys seeing it accumulate. Along with covering the trees, it seems appealing because of the very soft sound that the "downy flake" makes in the wind. The speaker mentions the dark quality twice: "The darkest evening" and "dark and deep." They indicate that the owner, and by extension may mean no one, will see them there. Their only companion seems to be the horse. If the speaker is headed for the village, it seems to be some distance away, as they have "miles" to travel. It remains ambiguous if this speaker is going to or from the village, so the woods' attraction seems related to its distance.