We have a new house, well built, spray foam insulation, tight seals. My daughter's room is over an unfinished area of the basement and is COLD this winter. There are vents in the unfinished area, but we have them closed because we don't want to heat that area. We probably wouldn't ever finish that room because it is our main storage space. The whole unfinished space is below ground. My husband and I are having a debate. Do we install foam board insulation on the walls in the un finished area or do we spray foam or use other insulation in the ceiling of the unfinished area? Or both? Our HVAC is not the issue, we have checked that out.
If the ceiling of the unfinished space is the floor of the bedroom and is uninsulated, the floor of the bedroom is going to be cold. It would help a lot if that floor was insulated. There is not any real downside to insulating that floor or the unheated space. Insulation on the walls of the unheated space would help a bit, but you will see much better results if you insulate the ceiling/floor first. Doing both would be great.
There is no point in insulating a cold unheated room! Concentrate instead on keeping the heat inside the warm bedroom. The best way to insulate a cold floor is, to lay sheets of tightly butted polystyrene or similar closed cell insulation on the existing floor and to then cover them with glued t&g oriented strand board. This way you have a fully floating floor, there are no heat bridges to syphon away your heat
To have a really warm floor (no cold feet) have sheet polystyrene, OSB, underlay, carpet. This will give you a carpet surface temperature the same as the room air temperature at floor level. ie; with an air temperature of 22C you will have a carpet surface temperature of 22C.