My furnace seems to be re-firing more often then usually. Other than the apparent, "it just got much colder out", could this be a problem with the thermostat?

Not usual unless the temp spread is large. If the temp is low outside and hot inside, it will run a lot.

What type of thermostat do you have? Is it fairly old? If it is an old mercury stat, it would be best to upgrade to an electronic or digital stat. If that doesn't solve the problem, let us know what type of furnace you have, make and model, etc.