Oh my gosh!! I am so surprised at all the posters saying this is fine!!!
It is NOT fine, whatever culture or country you are from (and ive lived all over the world ans have many EE friends ans friends from all over the place), to take a child out 2 or 3 times in the middle of the night to walk 2 or 3 miles in the cold. That is simply not ok, unless it's a one-off because, say, the child couldn't sleep or it was a special fun 'midnight walk' or something.
OP, you absolutely are right to worry if you have your facts straight.
That child is probably in school, or will be come September. How can they concentrate having been up half the night walking in the cold?
Children need a good nights, uninterrupted where possible, sleep.
Children need to be protected and kept warm on cold nights where possible.
OP, please don't listen to the posters saying this is fine. If you are sure of your facts, you need to mention this to someone (school? Social services advice line?) and if you are not sure but suspect, seek advice from say the NSPCC.
Poor little muppet.