Sadly, mushrooms are carbohydrate poor, but high in other nutrients.
They can be harvested year-round, but need several weeks to get started.
They need careful attention to the the growing environment, but this is also likely to be a place which will survive disasters which kill other crops. Think; a basement or below ground structure.
http://www.offthegridnews.com/survival-gardening-2/mushrooms-the-perfect-indoor-fast-growing-winter-crop/Should you chose to try this, I recommend that you start, now, with commercial starter kit which has the "spawn" and a starter growing medium. You will need to expand you mushroom beds with more growing medium to keep the patch healthy.
Recipes for growing medium are available online and are part of any good starter kit. Plan on this immediately because the starter kit will not have much medium.
I would start with the most common, white, button mushrooms and after you gain some experience, you can start looking for wild mushrooms to expand your variety.