Why does the speaker want to watch the “woods fill up with snow”?
There is also a sense that snow takes the "edge" off things. Some of the sharpness of "real" or "practical" life is removed, and things tend to blend together into one more continuous, more, as it were, "whole" reality where we are away from the practical. (This is hard to explain, but if you have ever lived on a farm, its something you have probably experienced.) Even the man's horse knows that it's "impractical" to stop "Between the woods and frozen lake/The darkest evening of the year." Sometimes practical may not be the most important thing. Perhaps the onness of this moment compensates for all the breaks in the "promises."
Despite this comfort, the real world beckons with its promises that must be kept and the miles to be travelled to keep these promises. But the snow is only temporary, and it must be "watched" while it can be ....
The motivation behind the speaker stopping to "watch the woods fill up with snow" is one of simple leisure and relaxation: He stops to watch the "easy wind and downy flake" not out of some great inspirational realization, but rather, to pause and reflect upon the beauty and simplicity of the snow among the woods itself. The entirety of this poem explains this idea with thorough lines that detail the author's frame of mind.
"The woods are lovely, dark and deep,/but I have promises to keep,/and miles to go before I sleep,/and miles to go before I sleep."
The author has other affairs to attend to, obviously, but doesn't mind pausing to enjoy the sight of the woods filling with snow.
On the contrary my dear engthcr5 and Tim, I think the answer is somewhat more straight forward and actually rather stark and poignant, hidden within the setting like a great but terrible secret. Yes the coating, edgeless quality of snow is at once soothing, and also very romantic. The narrator is reflecting on the world in flux, for the scene perfectly matches his heart, which is also in flux. He is under pressure, possibly simply the pressure of life. The end of the poem, "promises to keep" etc.. means that life must go on, and whatever pressure the narrator is under, he cannot simply stand by and watch and creep into the woods to be buried with the land while the world moves on. After all when the snow melts the land will return once again. But what he is contemplating is irrevocable. It is a poem about suicide: he is contemplating it and the horse and his promises represent both life's natural urge not to end itself and also the effect of his actions on others - friends and family etc... He realises he has "miles to go before he sleeps" - and in this moment as watches the snow cover the woods he has resolved that it is not his time yet (consider Eliot's Wasteland: "Winter kept us warm, covering earth in forgetful snow"). It is the darkest night and he knows he is alone. The poem has a very private feel, somewhat quasi-rhetorical on the part of the poet. The melancholy and haunting winter scene is an evocation of much earlier romantic poems, and though beautiful does not convey the complexity of the English romantics. A truly measured response might also consider Wordsworth, Keats, et al for top marks! Milford (a.k.a Milf).