In the first stanza the speaker tells why he is stopping by the woods. It is "To watch his woods fill up with snow." It is a cold night but apparently not too cold for the speaker to stop for a few minutes to look at a beautiful sight. I think all of us have done this at one time or another, though most of us were not riding in a horse-drawn sleigh. We are on a motor trip and see a beautiful view. There may even be a marked turn-off where motorists can park and enjoy the view. There are plenty of such places, for example, around the Grand Canyon and probably in every national park. Frost was a nature lover. He not only enjoyed looking at beautiful natural scenery, but he seems to have drawn inspiration for some of his poems directly from nature, as was also done by famous English poets like William Wordsworth and John Keats.
"Stopping by Woods on a Snowy Evening" reads like a tribute to the beauty of nature. If we get anything out of the poem at all, we get the feeling of being there on a cold, dark, silent night watching the "downy" flakes slowly descending like white feathers and settling on the trees. It would seem that these woods would have to be evergreens because the speaker says it is "the darkest evening of the year," which would make it December 21st or 22nd. At that time of year all the deciduous trees in the region would be bare or nearly bare of dead leaves, and this would not be a pretty sight. But evergreens with their widespread branches covered with snow are always so aesthetically appealing that they are often depicted on Christmas cards.
If the trees are evergreens, that would explain why the speaker seems apprehensive about being seen by the owner of the woods. That other man sees the woods as a commercial investment. If he found the speaker stopping there and looking at his woods, it wouldn't occur to him that someone was just enjoying the beauty of nature--especially on a cold night with the snow falling. Christmas is just a few days off, isn't it? Most people in New Hampshire probably don't go to some Christmas tree lot to buy their trees for the holidays. They probably go out and chop one down. The owner would undoubtedly think that the speaker--Frost himself presumably--was thinking of taking one of those trees home with him.
The plot of "Stopping by Woods on a Snowy Evening" by Robert Frost is quite simple. The speaker rides in his horse-drawn sleigh or carriage through the snow to the edge of the woods where he stops near a farmhouse and watches the snow fall for a time. While he is patient and unmoving, his horse is impatient and restless, jangling his harness bells as if to tell the speaker that he is more than ready to leave. That's it. Nothing more really happens.
The bigger question is the one you ask: why did he stop here tonight? This stopping place is clearly familiar to him, as he knows who owns this land. It is a spot close to civilization yet away from it, and the speaker obviously finds something about the darkness of the woods compelling. The lake is frozen, the snow has been falling, and the night is dark so the whiteness should shine even brighter; instead he is drawn to the shadowy darkness of the woods. Most of us would think all the glistening whiteness is beautiful; however, the only thing the speaker refers to as beautiful is the woods while they are inescapably, inseparably covered in glistening whiteness. To him,
[t]he woods are lovely, dark, and deep....
The horse is impatient to leave, but the speaker regrets not being able to stay--or at least he regrets having to go back to his "real" world. The final stanza of the poem gives us the best hint about why the speaker of this poem stopped here tonight to look at the woods.
The woods are lovely, dark, and deep,
But I have promises to keep,
And miles to go before I sleep,
And miles to go before I sleep.
Though he does not tell us explicitly why he stops, the speaker clearly wishes he could do something more than fulfill the promises he has made in life. He regrets that he cannot explore or get lost or do something other than what he has committed to do, the thing that is so wearisome that he has to repeat the fact that he has miles to go before he can sleep. It will be a long time before he can disentangle himself from the things he is bound to and the woods represent something about which he is wistful; however, he will fulfill his obligations and take the memory of those "lovely, dark, and deep" woods with him.
The speaker stops in the woods because in the second line of the poem he says he thinks he knows who lives in those woods, so he stops because of that. He also says that the person in the house will not see him stopping there to watch his woods fill with snow. The use of the word his suggests that maybe he is jealous of the person in the house, and he is resentful that he has to hide to watch because the woods don't belong to him, but to the man in the house. This reasoning also would assume that the man is probably poor and has lead an overburdened life.