What is the ruling on walking with one's hands clasped behind the back, and has any authentic hadith prohibited this?

There is no religious text that prohibits walking with hands clasped behind the back. Furthermore, this posture is common among people generally and is not specific to any particular group. Customs are, in principle, permissible unless there is evidence to prove their prohibition, according to what Sheikh Al-Islam Ibn Taymiyyah affirmed. Therefore, this posture in walking is permissible.