Is it cheaper to close doors and not heat unoccupied bedrooms in the winter months or should you heat them

It's going to be cheaper, but there are some warnings:

1. If too many returns are closed off the heating system (fan) can be damaged. A bypass damper will solve that. Some Carrier systems don't have this problem.

2. Put something under the closed door too to prevent air from entering the room.

3. Condensation can occur on the closed vents causing rust.

4. Furniture can be damaged if the temperature gets too low.