Is “Historically, Xuanzang did not ride a white dragon horse on his journey to the West.” true?

In Chapter 015 of 'Journey to the West', the son of the Dragon King of the West Sea transforms into a white horse to carry Tang Sanzang on his pilgrimage. According to 'The Biography of Master Sanzang of the Great Ci'en Temple', when Xuanzang left through the Yumen Pass, he rode an experienced old red horse, with no mention of a dragon horse. (Original text: 「这厮本是西海敖闰之子，他为纵火烧了殿上明珠，他父告他忤逆，天庭上犯了死罪。是我亲见玉帝，讨他下来，教他与唐僧做个脚力。」, source: data/raw/xiyouji/第015回.txt)