Adventures in Wonderland (1992)

S1E14 How the West Was Wonderland

A rodeo is heading to Wonderland, and the Queen is determined to be crowned "Queen of the Rodeo." However, she faces a challenge: she must ride a horse, which terrifies her. Despite her fear, her pride prevents her from confessing it. Meanwhile, Alice and the White Rabbit notice her dilemma and come up with a clever plan to help her maintain her dignity while tackling the situation.