The Story of Noah's Arc is pretty cut and dry. There aren't really any gray areas about who or what was on the boat. I do not recall God mentioning to Noah to be sure to save the root-n-est-toot-n-est cowboy in the wild wild west. As you can see, if it were up to Lula Mae Woody would have been the first to board the arc. All the cute little critters would have had to step aside for Sheriff Woody.
She really REALLY loves Woody.