Criminal law: No problem.
Civil law. (In theory): The writers of the letters retain copyright in their correspondence, so you must seek permission to publish the letters.
Civil law. (In practice): If you omit the names of the children writing the letters, it's unlikely that they'll recognise what they wrote, and they'd find it hard to prove that your publication contained anything which they held the copyright to. There's no legal aid for court action and any sensible solicitor would almost certainly advise against it.
Chris