It's not normal. The majority of people can't be bothered switching it on or off, so they just leave it on all the time.

Any HVAC system installed or revamped in the past 15 years is likely to have a programmable thermostat. Whether people are using these _correctly_ or not (which as others have touched on here is not necessarily super intuitive, part of the problem Nest is meant to solve), I think attempts of some sort at saving energy with these is pretty common.

Every heating system I have ever used has a double timer for two on off periods a day. But this is not in the US.