In "Frost at Midnight," Coleridge describes the place where he was living at the time—a cottage in Nether Stowey, Somerset, England, near the Quantock Hills. But he also reflects on his childhood, as a student at Christ's Hospital School in London, and his birthplace, way out on Ottery St. Mary, on the southwest side of England.
The setting plays a crucial role in the poem, since it deals so much with Nature, and with the differences between life in the city and life in the country. For Coleridge, being closer to Nature is like being closer to God. Nature, for him, is really a message or a revelation from God. On the other hand, being stuck in the city seems to be a boring and rather isolating experience. Child Coleridge hopes that an unknown "stranger" will suddenly visit him as he's sitting, daydreaming in class.
After describing the silence and natural stillness of life at his cottage (now known as "Coleridge Cottage" as a fairly famous tourist stop), and relating the constricting experience of his childhood in the city, Coleridge hopes that his baby son Hartley will lead a freer, happier existence in the country, communing with God and Nature. The poem definitely prefers this more rural lifestyle to the urban way of doing things, and it's colored by imagery picked directly from that location: lakes, mountains, clouds, frost, and icicles hanging from the cottage roofs. It sounds like a picture postcard.