The speaker of the poem, who is presumably Robert Frost himself, thinks he knows who owns the woods he has stopped to look at. The first stanza reads:
Whose woods these are I think I know.
His house is in the village though;
He will not see me stopping here
To watch his woods fill up with snow.
He is pretty sure he knows the owner, but he must not know him very well or he would be completely sure whether he was the owner of the woods. The owner lives in town and Frost lives in the country, so they would not be likely to be friends. However, the man Frost thinks owns these woods would recognize him if he saw him stopping to look at them. There is a certain air of mystery in the quoted stanza. Why should Frost care whether the owner sees him looking at his woods? In other words, why should Frost be particularly concerned about being seen by that one man and not by other passers-by? This is rural New Hampshire. Everybody knows everybody. Anybody who saw Frost stopped in that spot would probably recognize him. But Frost apparently is not concerned about being seen by anyone other than the owner of these trees.
The time is specified as December 21st, which is the "darkest evening of the year" because it is the longest. At that time of year the deciduous trees would have all shed their leaves. The only trees worth looking at would be spruce trees. Many people raise spruce trees in New Hampshire to sell them as Christmas trees. They are an important crop. Frost is stopping to look at the trees "fill up with snow" because it is a beautiful sight. But he knows that the owner of the trees would not understand that he was only enjoying an aesthetic experience. The owner would think that Frost was probably planning to chop down one of the saplings and take it home to decorate for a Christmas tree. People in rural New Hampshire surely do not buy their Christmas trees off a man in a leather jacket who is renting a vacant lot in some city or large town and living in a little trailer. They go out and chop down a tree. This is all right as long as they don't chop down a tree that some neighbor is raising to sell.
Perhaps Frost is a little worried about being seen by the owner of the trees because he has some notion in the back of his mind of doing just what he thinks the owner would suspect him of planning. It is but one step from admiring something to wanting to take possession of it. If Frost had sat there long enough he might have decided that one little evergreen tree wasn't going make any difference to a man who owned so many.
Frost once said:
Everything written is as good as it is dramatic. It need not declare itself in form, but it is drama or nothing.
Frost tried to make his poems dramatic, and he added a touch of drama to "Stopping by Woods on a Snowy Evening" by introducing the possibility of being seen by the owner, who might not be sitting by his fireplace in the village but might be out running errands, just like Frost himself. The owner would not have a poetic temperament or an appreciation of snow-laded spruce trees for anything except their commercial value. He would not understand that Frost was "just looking." What he would think would be that he had arrived just in time to save one of his saplings. Whether or not Frost might have been thinking of stealing a Christmas tree, the owner would tell other people about the incident, and it would hurt Frost's reputation. So there was just enough danger to make the little poem dramatic.