Watching snow pile up quietly, the speaker is reminded of a memory from childhood: their father reading aloud to the family. The link between the two is gentle rather than obvious. Snow changes the look of everything it touches, making the familiar "strange," and the speaker seems to feel the same hush and slow change in the memory of those evenings.
The details are small and soft. The father holds the book "in his lap," pages whisper as they turn, and nobody rushes. The last lines are the most interesting. Each listener builds "a picture / all our own," so the same story becomes a different private image for every person in the room. Snow does something similar, since it covers the same landscape but invites us to see it anew. The mood is calm, warm, and a little nostalgic, a quiet pleasure in being together while each mind wanders somewhere personal.