If you’ve just got a small colony of bees, I would hive them in a nuc until their numbers build up. I realize that could be a problem if you did a cutout and the combs aren’t perfectly flat and can’t be stuffed into a nuc. In general though a nuc is better for small colonies because it is easier to heat and it is easier to defend against pests and robbers.
If you go with a foam box over the hive, make SURE you leave a top vent in the foam and the hive. A vent about 1” x 3/8” should suffice. A foam shell gives the bees insulation, and it also completely cuts out any cold winds. Foam also slows how quickly temps can change in the hive. That could be good for the bees when an arctic cold front catches them by surprise. I would not think you would need very thick foam to be effective in southern OK. A hive wrap might be a good alternative for your southerly location.