In Dickinson's poem "We Like March", March is personified. (Personification is the giving of human characteristics to non-human and non-living things.) March is referring spring (the first day of spring is March 20th).
The reference to the color purple is made given
purple has a special, almost sacred place in nature: lavender, orchid, lilac, and violet flowers are often delicate and considered precious.
This definition of the color reiterates the use of it in coherence with springtime.
The entire poem is an ode to "March" and the coming of spring. March, given its ability to "make mud" references the spring rains which bring the flowers- many which could be purple given the shoes spoke of in the poem can be an image referencing the flowers which will bloom at the feet (on earth) of March.
Therefore, the color purple can reference two things. First, the flowers which bloom at the onset of spring. Second, purple's place upheld in nature as being special and sacred.