Robert Frost once answered a similar question with the statement: "If I wanted you to know I'd had told you in the poem." Feelings from poetry are intensely personal, and a poem that creates deep feelings in one may leave another cold. For "Stopping by Woods on a Snowy Evening," the feelings include nostalgia, desire, sadness, joy, appreciation of beauty... the list goes on.
The poem certainly has a hint of sadness in it. The narrator wants to sit and admire the woods, but he needs to travel to fulfil his obligations. He has no leisure time, and even his horse is impatient, wanting to continue. Life doesn't give people many choices, and many times pleasure must be put off for business. The narrator realizes this and deliberately steals some time to enjoy the sight of the snowy woods.
Another feeling that might be created is envy; the narrator is envious of the person who owns the woods and yet does not appreciate them properly:
Whose woods these are I think I know.
His house is in the village, though;
(Frost, "Stopping by Woods on a Snowy Evening," eNotes eText)
If the narrator owned these woods, he would live inside it, experiencing nature through his love of natural beauty. The reader is invited to sympathize with the narrator and develop a desire for a simpler life, devoid of the constant distractions of civilization and obligation.
In the end, the feelings that come from the poem are personal, and no two people will feel the same after reading it.