This is the first of three haiku from Clark Ashton Smith (CAS) that refer to the Auburn Foundation of The Religious Sisters of Mercy, an international order of Catholic women. According to their website:
In the early 1940’s the community moved to its present Motherhouse in Auburn. It was at that time that the community became known as the Sisters of Mercy of Auburn.
In a couple different reminiscences of CAS, writers have noted that he would jokingly refer to "The Nunnery of Averoigne" in describing his neighbors devoted to the consecrated life. For an example of such a memoir, see Rah Hoffman's "Letter on Clark Ashton Smith":
It's interesting that in "Spring Nunnery", CAS describes "the nunnery's cold / Walls" in contrast to the warmer phrases that end the poem: "the poplar-leaves unfold, / Plums are flowering." There's always a danger of over-reading, especially with a very short poem, but then again nothing is accidental in CAS' poetry, and one can detect some of his dislike of organized religion in speaking of the "cold Walls" that surround the contemplative Sisters.