I don't see any deeper nuance to the phrase . It literally means 'to wrap yourself up', or in other words 'to wear'. To me, it simply conveys that they were dressed in uniforms. You don't mention the source but I am assuming it is from a novel perhaps? As with English, writers often use alternative ways to express something if they feel it is too prosaic. If that were the case here, instead of using which is perhaps a little prosaic, the writer might have wanted to choose a more 'literary' phrase like .