I think the coldness in the house represents the somewhat "cold" relationship between the speaker, when he was a child, and his father. The speaker addresses the "chronic angers" of the house, as well as how he would speak "indifferently" to his father. He tells us that "No one ever thanked" his father for the loving actions of getting up early on Sundays—likely the one day a week that he didn't have to wake up early for work—and making the fires so that no one else had to endure the "blueblack cold" (which seems to suggest that it was so cold that it could freeze skin, turning it a frost-bitten black and blue). Not only did the speaker's father make up the fires so that the house would be warm for his family, he also polished the speaker's "good shoes," presumably for religious services. Now, as an adult, it seems...
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that the speaker recognizes "love's austere and lonely offices"—these things his father did to show his love. It does not sound like his father was openly loving or affectionate, or that he did anything warm and fuzzy to indicate his love; he showed his love in these other ways, and the speaker, when he was young, simply did not recognize that these were the ways his father showed his love.
Perhaps we can argue that the coldness in the house, so vividly described, represents the harsh reality of life in the poet's time. There are a number of suggestions in the poem that seem to indicate the coldness could actually be a symbol for something else. Consider the following quote:
...and put his clothes on in the blueblack cold,
then with cracked hands that ached
from labour in the weekday weather made
banked fires blaze.
It is highly significant that it is the father who faces the cold, whose "cracked hands" are already suffering from the extreme cold. It is he who makes the "banked fires blaze," the alliteration adding emphasis to this act of creating heat, and it is the speaker who, still in his warm bed, hears "the cold splintering, breaking." The narrator never has to face the cold in its raw intensity. This perhaps indicates that the cold is a symbol for the harsh realities of life that the narrator's father does his best to protect him from.