Why does the speaker stop by on the darkest evening of the year?
What seems to arrest the narrator as he travels through this forest is the incredible beauty of the scene around him. The beauty of the scene is enhanced by the stillness he feels, and this stillness is conveyed, in part, by the complete and unbroken darkness. So much of the poem is a play on and exploration of opposites: total darkness and the comparative light of the village where the owner of the woods lives, the silence of the woods and the bright jingling of the horse's bells, the tranquility of the idea of staying here forever and having to continue on for many, many miles. Perhaps the narrator would be less struck by the scene were the night less complete, less utterly black. He seems to stop on this night because the peacefulness he feels and beauty that he recognizes is so connected to the perfect darkness and stillness of the scene.
Though it is tempting to respond that it is impossible to know from the text precisely why the narrator of the poem has stopped, there is some evidence at the beginning that he's simply making sure of his surroundings:
Whose woods these are I think I know.His house is in the village though;
And miles to go before I sleep,And miles to go before I sleep.