Praise be to Allah, and peace and blessings be upon the Messenger of Allah and his family.
We have not come across any hadith which forbids placing one’s hands behind one’s back, with one holding the other, whilst walking.
One of the contemporary scholars was asked about this posture and he disallowed it on the grounds that this was originally the way of the disbelievers and that it is a custom that has been imported from them, and it is forbidden to imitate them.
We do not know of any evidence to support the view of the one who said that, and there is no argument to support it. This manner of walking is common among all people on earth, and it is not exclusive to some people only.
If there is no evidence to prove that a certain custom is prohibited, then in principle it should be regarded as permissible, and it should not be disallowed.
Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him) said:
The basic principle is that customs are overlooked and pardoned, and none of them is forbidden except what Islam forbids, otherwise we will be included in the meaning of the verse (interpretation of the meaning): {Say, “Have you seen what Allah has sent down to you of provision of which you have made [some] lawful and [some] unlawful?”} [Yunus 10:59]. Hence Allah condemned the polytheists who ordained matters of religion for which Allah had not given permission, and they prohibited that which He had not prohibited… This is an important and useful principle."(Majmu‘ al-Fatawa 29/16-18).
And he (may Allah have mercy on him) said:
I do not know of any difference of opinion among the earlier scholars that if there is no evidence to prohibit something, then it is permissible and is not to be restricted. This was stated by many of the scholars who spoke of the fundamentals and minor issues of religion, and I think that some of them mentioned consensus on that matter, either on the basis of certainty or near certainty."( Majmu‘ al-Fatawa 21/538).
So the basic principle is that this manner of walking is permissible, because there is no sound evidence to prove that it is prohibited.
And Allah knows best.