Like the even older Anglo-Saxon riddles (which may well have influenced them), these poems have an archaic power. The lines about the rooster make me shiver also. I think it might be because such riddles tap into a root of poetry itself, the power to make ordinary things portentous. Once the solution is found, the answer enhances the mystery of the puzzle rather than diminishing it, as happens in a typical contemporary riddle--so all the power of the previous not-knowing accrues to the rooster, making him even more mysterious and resonant a symbol than he was earlier.