I live in a heavily wooded area. In fact, we can gather enough standing dry wood in an hour's foray into the woods for an all-day (eight hours) sap boiling session. And this wood is "seasoned" - not green wood. In short, for the past several years we haven't cut any trees to boil maple sap, and we haven't used any of our firewood, either.
For me and others who live in my climate heating and cooking with wood is a very simple matter of knowing what wood will burn right now, and what needs some time to dry and season, and it takes very little energy (in the form of fuel) to get wood from its place of origin to my house - i.e. no gas-powered vehicle needs to even enter the equation. For us, it just a simple matter of walking into the woods and picking up sticks - and those sticks are sometimes not sticks, but rather sapling-sized deadwood that would simply rot. In my area, we could gather a whole winter's worth of wood, one wagon load at a time. It would take every spare moment we had all spring, summer and fall, but it could be done without dependence on fossil fuels.
I'm not so naive as to think that my particular circumstance is true of everyone everywhere. Wood is the best fuel source in my area, but not everyone lives half in the woods, like I do, and I'm well aware of that fact.
There are many options for heating and cooking that don't require much - or any - wood, and I touch on most of the known ones in my book.
For those people who have a few trees that could be coppiced (or would need annual pruning anyway), a rocket stove might be the best choice for cooking. Rocket stoves use very little fuel, but can reach extremely hot temperatures. Coupled with a cob oven, which also uses little wood, one would be able to cook just about anything with just a few twigs. If I lived in a suburb more south of where I live, and I didn't have very many trees, I wouldn't want to cut down all of my trees to cook my food, and I'd certainly be looking into building a rocket stove and/or a cob oven.
Rocket stoves aren't just tiny cookers, and in fact, aren't just for cooking. The technology was being developed in the 1970s, but today's volatile fuel prices have seen a resurgence in the interest in low-energy heating options, and I'm seeing a lot of articles and stories about people designing and building rocket mass heaters, which are an incredibly ingenious marrying of the rocket stove and the age-old European masonry heater, which I think are just beautiful. If I could retrofit my house for a masonry heater, it would have been done already.
I like the super fancy, aesthically pleasing masonry heaters, but they don't have to be fancy to work well. When I was doing my own research on different heating options, I found a story about how those living in extremely cold environments where there were very few trees, like north central Asia, and basically, their heating solution amounted to building a fire on a masonry shelf. The idea was, at its core, the same idea that has created the rocket mass heaters, and that was to heat up a thermal mass. In this case, the fire was built on a stone shelf. When the fire had burned down to coals, the ash and coals were scraped off the shelf (and the coals were probably buried in the ash to save for lighting the next day's fire), and the people slept on the warm shelf.
For those of us in our suburban homes, where we don't have thermal mass heaters or wood to burn, other options will need to be explored, most of which I've previously discussed, as well.
For those with no wood, solar ovens are very popular - and one doesn't have to purchase a commercial model (spending hundreds of dollars). Dan and Beth Halacy's book Cooking with the Sun gives some great instructions on DIY solar cookers - and not just ovens, but also a solar hot plate.
I've researched other options for cooking and heating that don't even require wood. My favorite is a methane digester, which uses organic waste (could be yard waste, kitchen scraps, chicken manure, humanure) to create an anaerobic reaction and produce methane, which can be burned and used to cook or heat a space.
For cooking or heating very small, very well insulated spaces (like with a kotatsu), something as small as a sterno can might be enough.
There's one other heating/cooking option that I've, since the publication of my book, discovered. It uses the sun and a very simple, fairly inexpensive fresnel lens (it's pronounced /frā-něl'/ - long a, s is silent).
The most popular, current, application for the fresnel lens is a steam generator, but the basic concept is to heat water - which means, it could be used to cook, also.
Check out this video. There are several other videos, too. I recommend watching as many of them as one can.
Michael Douglas, who is a teacher at the Maine Primitive Skills School, recommends perfecting as many methods of making fire as are available to us, and I agree. In fact, I would apply that logic to other things, as well. It's wise to know several ways to preserve a certain food item, and it's valuable to know many ways of cooking a thing - in case one of those methods fails or is unavailable.
We use wood for all of our heat and for much of our cooking during the winter, because wood is what we have. We also use matches to light fires, because they're available, but we also know a lot of other ways of making fires ... and we know a lot of other ways to cook food and heat our home.
If I lived in a less wooded environment, I wouldn't be relying on wood for heating or cooking, and I'd be exploring some of the other options I've mentioned in my book or here on my blog. If I lived in a warmer climate, even if I had access to as much wood as I have here, I'd be looking at a methane digester, and if I lived in a very hot climate, without wood, I'd be getting myself a fresnel lens ... taking extreme care where I pointed it.