Why does the speaker mention the woods' owner in "Stopping by Woods on a Snowy Evening"?

By bringing up the owner of these woods, the speaker in "Stopping by Woods on a Snowy Evening" establishes a contrast between those who immerse themselves in the beauty of nature and those who are content to live in the "village," presumably surrounded by people and busyness.

The owner of these woods is not a farmer or a rural resident; instead he owns this seemingly expansive stretch of land while living in a more "civilized" area. He is presumably some sort of business man; the fact that he can acquire parcels of land separately from his own residence indicates that he is of elevated economic standing. It can therefore be assumed that the owner has some degree of influence in their community, and trespassing on his property therefore increases the tension of the speaker's choice to pause in this spot. The speaker is thus uninvited and seemingly unwelcome here, yet he longs to absorb the beauty of this wintry scene for as long as possible.

Does the owner of the woods matter in the first line of "Stopping by Woods on a Snowy Evening"?

The first stanza of the poem by Robert Frost "Stopping by the Woods on a Snowy Evening" 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.

The poet, which also serves as the main character of the poem who is experiencing the situation, apparently is a peasant or a commoner who happens to be walking through a patch of land that is owned by someone who is known by him. If this landowner is well known enough to be recognized, or thought to be recognized by this commoner walking his woods, then it can be safely assumed that this landowner is well known per se. Therefore, this well-known or partly well-known landowner must have some power over the common man: He owns something that not many other people can have. Something that is beautiful, and uniquely belonging to him.

The feeling that the poet brings out in admitting that the woods belong to someone else place him in a distant and isolated position, regardless of whether he is actually there in front of them. He cannot love them too much because, though they are naturally free for anyone to admire, they are still someone else's property.

Yet, the poet allows himself to admire them, regardless. This is a symbol of the small freedoms that, even those who seem less worthy of the beauties and benefits of life, give themselves to make their lives more colorful.

He, who cannot stop by the woods for too long, indulges in the small freedoms that nature provides,along with the gifts that it offers us in the form of the elements: Snow, the sun, the rain, the dew. All these compose an everyday ensemble that provides a background for everyone's life.

Therefore, as far as how the poet perceives the ownership of the man who owns the woods that he loves, we do not see resentment, as much as we see longing. We see that he longs to be able to enjoy the woods, and it would be an everyday blessing for him to be able to enjoy the sight everyday: But the woods are neither his, nor part of his journey- for he has "miles to go before he sleeps".