My sims get the chilled moodlet only when its freezing outside. The warmth from a fireplace only travels so far. I notice the moodlet goes away if I have them sitting or doing something close to the fireplace. For example, they have an open concept floor plan and the fireplace is in the "living room" area, if they are over in the kitchen area then they can get the chilled moodlet again. This doesn't happen in smaller rooms though. If there's a fireplace in a small room it will usually heat the whole area. For example, they have a fireplace in their master bedroom, if they are in there they never get the chilled moodlet.
Sometimes I just use the thermostat. I only use it when the temperature is freezing, and as soon as it warms back up to cold, I turn the thermostat off. My bills are only about $4,000. They do live in a 5 bed 4 bath house though, so I think this is very reasonable.
Also, I have one outfit in the cold weather category that is just a warm outfit they can wear at home. For example, the teen in the family has one outfit that is just sweat pants and a sweater with socks on. This will register as a warm outfit and get rid of the chilled moodlet. If they wear it outside I just change them into normal outdoor clothes. It helps if the outfit is #5 on the category list, they don't seem to pick that outfit themselves too often.
