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.
The little horse must think it queer To stop without a farmhouse near (5-6)
How does the little horse know there isn't a farmhouse near, and, more importantly, why does the speaker choose to stop so far away from any other humans. The farmhouse represents something different than the village does – it's a bit more nature-loving than the village. But the one thing that both farmhouse and village have in common is people, and that's the one thing that our speaker doesn't seem to like too much.
But I have promises to keep, (14)
The word "promises" is an interesting one. Promises usually involve other people, and they usually involve the future (whether immediate or distant). In this way our speaker seems to be choosing people and his future over nature and the present.