Hints:

"blows his nail"—blows on his hands to warm them
"keel the pot"—cool the contents of the pot by stirring or pouring in something cold
"saw"—speech or sermon
"crabs"—crabapples
This poem describes an extremely cold winter and the problems which poor people face.
They have to go out and work in a weather in which water freezes while it is dropping from the wall.
(And Dick the shepherd blows his nail) it means that he blows on his hands to warm them so we can get from this line that they are so poor and do not have suitable facilities to warm themselves.
(While greasy Joan doth keel the pot.) Referring to the hint she cools the content of the pot, in my opinion there is paradox between the hot food, the cold weather and making the hot food a bit colder.
Despite the harsh coldness they do not stop their daily life. They still go to church even when most of them all sick. We can get they are sick by this part: (And coughing drowns the parson’s saw) it means people hardly can hear the parson's voice because of the sound of their coughing.
(When roasted crabs hiss in the bowl) crab is such an expensive food but here crab means crabapples. Since they are poor they have to eat roasted apples.





winter: is a symbol of death
Milk comes frozen: irony (irony of harsh coldness)
Owl: symbol of knowledge (the wise owl gives tidings of spring)
Merry note: irony ، because people believe that the owl tone is scary and gives pessimistic feeling of death
Roosted crabs: irony (because the people are poor and cannot have roosted beef so they have roosted crab instead)


Setting: gloomy
Time: winter
Place: poor village
Its theme: hope. Because despite of harsh coldness, drudgeries and hardships in winter the song of the owl is a merry note for them.