You can ice fish 24 hours a day in NH during ice fishing season. There are no restrictions for hours of day or days of week.
You can have holes in the ice 'within' your bob house so long as you are following the laws regarding number of lines etc.
If F&G are checking bob houses in the middle of the night,
they will knock. At that point you are awake and can unlock the door.
Nothing illegal about it.