You'll have less to worry about if your kids can stay warm, even if there's no heat in the house. When I was growing up, it seemed that the only sleeping bags available were these ugly army-issue kinds in olive green and khaki. A lot has changed since then, thanks to the revolution in hi-tech camping equipment. Most modern sleeping bags are made of advanced synthetic fabrics that will keep you warm even if they get wet, and they're designed to dry as quickly as possible. Many are also machine-washable, but be sure to check the label before you buy.
Some purists swear that down sleeping bags are the best, and it is true that down is very warm.
Whether down is actually better than synthetic is debatable. If you're allergic to down, obviously, synthetic is the way to go. Also, if a down bag gets wet, it won't keep you warm like a synthetic bag will and it takes a lot longer to dry. The bag is kept closer to the body, thus conserving more heat, and it's lighter and easier to transport. Another important point to remember is that sleeping bags are rated according to the lowest temperature at which they will keep you warm.