The batteries and the filter should be changed on a regular basis. Don't know what kind of batteries they are, but follow the recommendations from the manufacturer. The filter should be changed yearly. They are not that expensive and you know how to do it yourself. What kind of furnace do you have? If you have an oil furnace, it would be worth learning to change the oil filter as well. It makes the furnace run more efficiently. Around here they charge about $100 for the servicing that basically just means cleaning/changing the filter.
Some electric companies will do a free energy assessment and make suggestions about how to better insulate your house. If I remember correctly, the weatherstripping around your front door needs to be replaced. One of those draft snakes for the bottom of the door helps, too, and they are dirt cheap.
The plastic window covers for bathrooms are dodgy. I've never been able to get one to stick in our bathroom, but the windowsills are shaped oddly - it's an old house - and they don't make a good seal. Plus the humidity messes with the adhesive.
For the future, consider making window covers that would go on the outside for downstairs, with screws or perhaps latch hooks. Inside covers have to be pretty snug to keep drafts out, outside ones don't have to be as tight.