With brood (baby bees) I would not open up the hive again until it gets much warmer.
Then, this is what I would do. I would take the empty box off and clean it all up. Get it ready for the bees to move in to it.
Next I would determine if the brood was in the first or second box. Which ever the brood is in, place it on the bottom and the cleaned up box on top. Take the other box and clean it up.
Hopefully by now the weather would be really warm and the bees out working. I would then move the first cleaned out box to the bottom. Place the second cleaned out box on top of that with no frames in it and start pulling the frames one by one and cleaning up the burr comb on it, try not to rip open any brood, and place them into the empty box. Then set the now empty box on the top and place the other cleaned up frames in to it.
You might run into the problem of having some brood in the second box you wish to clean up. I would pull the frames on it while still at the hive and if there is brood would place those in the first cleaned box you now have on the top.
Another option would be to get more equipment while it is cool and set it up beside the old hive. Then pull the frames one by one, clean them, and place them into the new boxes.
It depends on how cheap you want to go. With the new equipment you might can do the whole thing in a day. If going one box at a time I would do one box a week.
I'm sure others here will disagree with me.