Heating and Cooking
If you're in an emergency situation with a dropping environmental temperature, you're in danger of hypothermia. Symptoms of hypothermia are slurred speech, slow breathing, cold pale skin, shivering, loss of coordination, fatigue and lethargy. One danger of hypothermia is that when you have it, when more body heat is lost than you can handle, you are not aware you're in danger. You think you're getting warmer but your temperature is actually dropping,
The first thing to do is to get out of the cold, and change into warm, dry clothing. Do not apply direct heat to the extremities (hands and feet. This would force cold blood back into the core, and drop the body temperature even more.) Do apply a gentle heat (such as a compress) to the trunk. (The condition of hypothermia forces the blood in toward the internal organs. Gently warming the torso signals the body that it can recirculate blood to the extremities.)
This brings us to a crucial issue: heating your emergency shelter. If you are using a shelter-in-place, you have to make do with dressing warmly, since your ventilation system will be blocked off by vinyl or plastic. Layering dry clothes will keep in body heat. Cover the head and feet, since that is where most heat loss occurs.
Options for Heating
Your primary objective is to prevent loss of body heat. Down or fleece is good for insulation. A mylar blanket is also useful. Thermal mattresses and thermal ground cloths can prevent dangerous body heat loss. The entire family unit should stay in the same room--preferably a room that receives sunlight in the daylight hours. Putting everyone in the same room will conserve body heat. Include pets. (Both dogs and cats have body temperatures that are a few degrees higher than humans.)
If you're not sheltering-in-place, and there is ventilation for a fire, a wood burning stove is useful. Exercise care in using a wood-burning stove or fireplace. Use wood. Do not burn charcoal. Charcoal produces toxic fumes. (Carbon Monoxide.)
Options for Cooking
Camping Stove (Sterno)
Sterno is known as canned heat--a jellied alcohol that is burned directly within its packaging. Campers use this, but the country club set also uses this in their buffet-style spreads. Under the chafing dishes, you will usually find food service industry standard sterno cans. At hiking supply stores, outdoor stores and on the internet, you can find sterno and specific "stoves" designed to support cookware above the sterno heat source. Provide adequate ventilation when burning Sterno.
A candle stove comes with a long-burning canned candle. It's very simple to use. Just light the candle and place it under the frame that comes with it. The candle heats the food. It's not a huge source of heat but it will adequately warm food. Plus if you use it judiciously, it can last a very long time--mostly because you can put out the candle and reuse it. There's no waste. The package usually comes with multiple wicks. Use one wick for light, two for cooking. The biggest benefits are that these candles are odorless, non-toxic and have no ceiling on their shelf life.
Pocket Stove with Fuel Tablets
There's a class of small cooking appliances called pocket stoves marketed at camping stores. They're small enough to fit in a pocket--or backpack--and use high performance fuel tablets. Some of these "stoves" are little more than clips that hold the fuel; and some are a bit larger, designed to safely support a cup or pot or can. Provide adequate ventilation when burning fuel tablets.
Coleman (TM) Stove
At the risk of name dropping, there's no competition for the Coleman stove. The Coleman Stove you think of first is a familiar green packaged stove set in a little portable "briefcase" which opens to reveal one or more burners. These stoves have earned the reputation of being reliable, affordable and efficient. Coleman stoves burn propane or liquid fuel, some of which are designed to use either fuel. There's a variety of these stoves available, so you should look carefully before you select what options you wish to use in your emergency shelter. Provide adequate ventilation when using a stove.