Well, it is important to identify one crucial difference between these two poems. We know a lot more about the parent in "Mother to Son" because she is the one speaking, whereas in "Those Winter Sundays" we only see the father through the son's eyes. This is crucial, as we never hear the thoughts and perspective of the father, and only see his demonstration of "love's austere and lonely offices" through his self-sacrificial act of getting up first in the house on Sunday mornings and lighting the fire so that the house is warm for everybody else. Clearly, the speaker's father is a man who is willing to sacrifice his own comfort for that of his family, even though he is described as having "cracked hands that ached" from his harsh labour in the cold. He is presented as a silent, unprotesting man, who does not begrudge his children this luxury, even though they do not even thank him for what he does.
The mother in "Mother to Son," however, clearly states repeatedly that "Life for me ain't been no crystal stair." She goes into great detail about how hard life has been for her, but at the same time, although she discusses the harshness of life a lot more than the father in "Those Winter Sundays," at the same time, she does go on to give her son a very important message:
So boy, don't you turn back.
Don't you set down on the steps
'Cause you finds it's kinder hard.
Don't you fall now--
She urges her son to keep on climbing up the staircase of life, not looking back or being tempted to stop and sit, hopefully trusting that things will get better and better. Both parents then through their words and actions teach their sons a very important life lesson. In "Those Winter Sundays," the son learns about the truth of what sacrificial love really looks like. In "Mother to Son," the son learns about the struggle of life and the importance of keeping on going.