The horse thinks it is "queer" or odd to stop in the middle of the woods because it seems his owner never does this. We know this because the speaker tells us that his "little" horse is used to stopping near farmhouses.
This would suggest that the narrator is a social person who primarily uses his horse to take him to and fro to visit people. This idea is reinforced by the last lines of the poem, in which the speaker states he has "promises" (social obligations) to carry out that are forcing him to move on.
Frost uses the reaction of the horse to help characterize the speaker, emphasizing how out of the ordinary it is for this man to stop in the middle of the woods to contemplate the beauty of the falling snow.