In the first line, the poet does what poets often do. He changes the orders of words in a sentence from the order we would usually use. We might say, " I think I know whose woods these are.How does the poet say it?

He says, "Whose woods these are I think I know." I think Frost was going for both rhythm and tone. Frost writes this poem in what is classically known as a Rubaiyat Stanza which are structured in quatrains. Note the careful placements of the rhyming words in the first four lines,

Whose woods these are I think I know. A

His house is in the village though; A

He will not see me stopping here B

To watch his woods fill up with snow. A

The tone feels gentle in it's carefully rhymed and gentle accents.