... You really want to get this trophy on purpose?
... You sure?
... Okay then...
As taken from the Book of Secrets:
"Goats eat flowers and then poop. Why? Because they are goats. Stop trying to change the world."
As suspected: Throw a flower to a goat and the goat will eat the flower. Wait a tic, and the goat will poop. Pick up the poop to get the trophy.
As long as you're doing this, make sure to bump into the poop for a Book of Secrets entry. If you wait a while the poop will turn into a snow flower, earning you another Book of Secrets entry.
I also noticed that if the goats don't come and eat the snow flower, the snow flower will keep on multiplying. What's more, as soon as there's five or six sunflowers in one area, it becomes sunny (so you don't lose energy while moving stuff).