1st read, 'of' was not proper, shoule be 'in', spring rain or rain in spring.
2nd read, 'of' makes sense if spring is a metaphor (such as memories),
or if it is read as Rain of spring music, falling, green & serene...
I felt the word "me" needs no "", leave it to readers' imagination.
I felt the word 'smile' is redundant, again less is more.
Since it is a short poem, every word counts. I modify it to rhyme both ways so that you can read it top-down or bottom-up, also more balanced.
Spring Rain
Rain
of spring
music falling
green & serene
as I listen . . . . . . . . . . . . .
me into you stepping
umbrella-less
soak-ing
Rain