The wheelbarrow symbolizes several different things in the poem. On the one hand, the wheelbarrow can be taken as a representation of farm life in general, especially when placed in an environment with "chickens." The fact that the wheelbarrow is also a tool might also indicate to the reader that the wheelbarrow is representing farm workers more specifically. By declaring that "so much depends upon" the wheelbarrow, then, the poem implies the importance of agriculture and farm laborers.
More broadly, the wheelbarrow can also act as a representation for any and all everyday objects that the speaker believes are deserving of appreciation. The wheelbarrow is a rather mundane item that people may overlook, and by focusing so intently on it, the poem might be suggesting the value of appreciating these simple items that make life easier.
To that end, the red wheelbarrow can also be seen as a symbol for perception. The speaker spends the poem altering the reader's perception of the wheelbarrow, which could suggest that the wheelbarrow is meant to demonstrate how one can—and perhaps, should— take a closer look at their surroundings and challenge their own perspective.