A disponibilidade dos livros de Oz em formato eletrônico facilita esse tipo de pesquisa. Eu fiz uma pesquisa rápida em todos os livros de Oz que eu tenho e encontrei muitas referências, apesar de muitos dos hits serem para a palavra "urso" como verbo.
De qualquer forma, em vez de passar anos analisando todos os resultados da pesquisa, parei na primeira menção de um urso. No livro 4, Dorothy e o Mágico de Oz, existem ursos invisíveis que se tornam visíveis quando mortos:
As the little Wizard turned to follow them he felt a hot breath against his cheek and heard a low, fierce growl. At once he began stabbing at the air with his sword, and he knew that he had struck some substance because when he drew back the blade it was dripping with blood. The third time that he thrust out the weapon there was a loud roar and a fall, and suddenly at his feet appeared the form of a great red bear, which was nearly as big as the horse and much stronger and fiercer. The beast was quite dead from the sword thrusts, and after a glance at its terrible claws and sharp teeth the little man turned in a panic and rushed out upon the water, for other menacing growls told him more bears were near.
Não encontrei nenhuma menção a tigres além do tigre faminto.
Mais tarde:
Os eventos do livro 4 acontecem na Terra dos Manaboos, não em Oz. Há uma menção indireta no livro 5 The Road to Oz:
"I am not so sure of that, sir," answered the Tin Woodman. "A while ago the crooked Sorcerer who invented the Magic Powder fell down a precipice and was killed. All his possessions went to a relative – an old woman named Dyna, who lives in the Emerald City. She went to the mountains where the Sorcerer had lived and brought away everything she thought of value. Among them was a small bottle of the Powder of Life; but of course Dyna didn't know it was a Magic Powder, at all. It happened she had once had a big blue bear for a pet; but the bear choked to death on a fishbone one day, and she loved it so dearly that Dyna made a rug of its skin, leaving the head and four paws on the hide. She kept the rug on the floor of her front parlor."
Alternativamente, no livro 11 The Lost Princess of Oz, existem vários ursos, embora não tenha certeza se isso é estritamente falando em Oz.
Aha! O livro 13 The Magic of Oz acontece na Floresta Gugu, que se diz ser:
the home of most of the wild beasts that inhabit Oz
e, portanto, presumivelmente em Oz. Nesta história, encontramos Bru, o Urso.