Back in the olden days, bards used to roam from town to town, singing songs to general public. You could think of them as the movie theaters of their time. Lots of the poems that we read on the page were once read (or sung) aloud. What's more, alliteration was one of the ways that bards would be able to remember lines, which is perhaps why Cummings decided to stuff his poem full of this literary technique. The images that attract the most alliteration tend to be of the figures of the hunter, the dogs, and the deer—in other words, all the living figures in the poem. Cummings: what a cool and crazy cat.
Lines 1-2: The G's in "green," "gold," and "great" connect the horse and its rider together through this sonic overlap.
Lines 5-9, 16-20, 26-28: Every time Cummings describes the deer, they tend to come in alliterative pairs. Funnily enough, though, the alliteration never repeats itself. Cummings is better at this descriptive language than most people we know!
Line 11: The alliteration here describes the huntress, loaded and ready ("Horn on hip").