Whose woods these are I think I know. (1)
Can someone can own woods?
His house is in the village though; (2)
Besides messing up the iambic tetrameter (check out "Form and Meter"), what would be lost if Frost omitted the word "though" from this line? What does that "though" imply? The owner of the woods owns lots of things. Things like woods and a house. He must be living the life. He must also be kind of disconnected from the natural world if he doesn't even want to hang out with his trees.
He will not see me stopping here To watch his woods fill up with snow. (3-4)
Mr. Speaker, you've already told us that the owner of the woods lives in the village. Why are you so paranoid? Also, why are you watching woods fill up with snow? To each his own – we endorse snow watching, if that's what you like. But, we're just curious about why you like this pastime so much.