Advantages of solar cooking, compiled from different sources (sources are cited at the bottom.) Since we’re only interested in the environmental (and perhaps some economical) aspect, I left out the social/health/other reasons.
Also, might want to have a look at this which claims to be:
more convenient, much lower-priced, and now competitive with alternatives such as wood, charcoal, and wood stoves. One such model, an open reflector, has been widely tested and has proven useful in the USA, Kenya and Zimbabwe. It pays for itself in fuel savings in two months or less and becomes a recurrent economic benefit to individual households.
It’s called a Cookit.
By the way, here’s instructions on how to build your own solar cooker:
http://www.charityguide.org/volunteer/fewhours/solar-ovens.htm
Sources:
http://solarcooking.wikia.com/wiki/Advantages_of_solar_cooking
http://en.wikipedia.org/wiki/Solar_cooker#Environmental_advantages
http://www.energieinfo.de/eglossar/solar_cooking.html

Firstly, the cooker must have some materials to shape it and give it structure, and to make it more durable. Materials that can be used to give it a box-like shape are wood, metal, clay, cement, almost any material that is stiff, although it must be moisture resistant. This is because when the food is cooked, water evaporates, and may condense on the outside of the box.
Secondly, insulators are needed to retain heat from the sun as food does not cook in a millisecond. Putting the insulators around the box allows for more even heating and also minimizes the heat being conducted from the inside of the box to the outside, thus retaining more heat. Some possible insulators are aluminum foil, feathers spun fiberglass, cellulose, wool, straw, and crumpled newspaper.
The top of the box must be covered by a transparent material to allow the sun rays to pass through and a greenhouse effect can occur in the box, which will raise the temperature in the box. Glass or plastic can be used. Reflectors should also be used to bounce more light into the solar box to increase the temperature.
Lastly, the insulators and the inside surface of the cooker must be moisture resistant too. The water that evaporates from the food when it is heated will condense inside the cooker as it is sealed. The moisture resistance will prevent damage to the materials.
How should the cooker be designed?
Ideally, it should be rectangular shaped and not too deep. This is to maximize the surface area for solar collection to volume ratio. It also makes sure that less heat is lost. Also, it should be easily movable, as it will need to be moved in accordance with the sun’s rays.
Is it feasible?
According to research, the time taken to cook a particular food in a solar cooker would take twice as long as that in a conventional oven, but the food will still cook. However, if there is no sun, the solar cooker will not work. Hence, it is greatly dependent on the weather.