Just taking a quick look here, we notice that a lot of stuff in this poem is frozen and-or cold: icicles, milk, blood, snow. Well, gee, this is because it's winter, and that's what happens. (Correction, that's what happens during a real winter, not the low-of-60 winter you get in some places like Arizona.) In this poem, further north, winter freezes all kinds of stuff that's associated with life: water (icicles, snow), blood, and milk. But this doesn't mean life has disappeared. No, no, no. The people in this poem have managed to adapt (they build fires, they cook), as have the animals (well, the owl seems pretty happy). As Dr. Malcolm says in Jurassic Park, "Life, ugh, finds a way."
Line 1: Icicles hanging, one of the most common images of winter. In fact, they pretty much symbolize winter.
Line 2: Dick the shepherd blows his nail, which is saying that he blows on his hands. "Nail" here seems to be standing in for "hands," which makes this an example of synechdoche. The dude blowing on his hands to keep warm is another very common symbol of cold weather.
Line 4: We're more accustomed to frozen water (like the icicles in line 1), but milk works, too. Milk symbolizes life and nourishment, and the implication here is that winter somehow temporarily stops or freezes life.
Line 5: Continuing with the life-itself-is-frozen motif, here "blood is nipp'd," meaning it is cold or perhaps metaphorically frozen.
Line 9: This is an interesting moment. It's freezing outside, yet "greasy Joan" is stirring ("keel") the pot in order to cool off whatever is in it. You can't eat stuff that's boiling hot, can you?
Line 12: Birds are sitting in the snow. Life is still… well, alive. The snow (semi-frozen water), like the icicles, is a very common symbol of winter.
Line 18: As in line 9, "greasy Joan" is making her pot a little more wintry by cooling it off.