My house has cold floors, and my energy bill is high – could it be the crawl space?

I've noticed for a while now that the floors in our house, especially on the first level, are always surprisingly cold, even when the heating is on full blast during winter. This also coincides with what feels like an unusually high energy bill. I'm wondering if there's a connection between these two issues and if it could stem from something beneath the house. Has anyone else experienced cold floors and high bills, and traced it back to problems in their crawl space or similar areas?