Will new roof shingles help with heating?

In General, NO. The Roof and Attic Spces below it should be insulated from Heated spaces inside your home according to local building codes. The attic and roof spaces must also be vented properly with soffit and ridge or power vents s cold attic in the winter will keep ice and snow from melting under the courses of shingles. A well vented, cool attic in summer will dramatically lenghthen the lifespan of asphalt based roof coverings.
The interior spaces of your house should be insulated and sealed/vented according to local building codes and by licensed professionals. For a roof, the colder the better, all year.