In a common wood fire such as a campfire, is matter converted to energy or is it simply an exothermic chemical reaction and all the mass can be accounted for in the ash and soot?
This is a common question that applies to chemical reactions, batteries, and other common forms of energy conversion. The short answer is yes, but of course the change is negligible.
In a chemical reaction you have a set of reactants and a set of products. If you were to take the mass of the reactants and sum them up, you would find them to be more than the sum of the mass of the products. This mass difference time $c^2$ is the energy of the reaction. Again, this is by an amount that is so small that it is unmeasurable. The mass change from of nuclear reactor fuel after burning it at a large heat rate for 4 years is barely measurable itself, if you're talking about putting the fuel on a scale and measuring it.
Now come the qualifiers. If you put air and wood in a completely closed container and let it burn what would happen to the total mass of the container? It would stay the same. The temperature would increase, and as the molecules move faster the mass increases (basic relativity). If you preformed a chemical reaction, then cooled the products, you could try to measure a mass difference that is theoretically predicted. But even assuming you have a scale that is precise enough, you'll have to look into other things like tidal forces. Experimentally measuring these mass changes would be a futile effort.