Before we can discuss the tone used in any specific poem, we need to establish what tone is in the context of poetry. In a nutshell, tone is the general attitude of the writer as depicted in the words and structure of the poem. In other words, the tone is the character of the poem. To provide a few generic examples before discussing the poem at hand, a poem can be cheerful, somber, humorous, formal, informal, admiring, or critical.
I would argue that the tone used in this particular poem is colloquial and instructional. Since this is a mother speaking to her son, it is quite natural for her to use a colloquial tone, and this tone comes across thanks to the use of incomplete words such as “a-climbin’,” “reachin’,” and “turnin'," She refers to her son as “boy,” which is a colloquial term of endearment. She speaks in her natural voice with no pretense or inhibitions, using the word “I’se” instead of “I am,” which adds to the colloquial feeling of the poem.
Through her colloquialism, however, the speaker is issuing her son with firm instructions. After using an extended metaphor to describe the difficulties she has faced in life, she issues her son with three instructions: “don’t you turn back,” “don’t you set down on the steps,” and “don’t you fall now.” The mother’s determination to provide her son with encouragement and teach him about life creates an instructional tone.