how much it costs will depend on what you feed. A high quality food is more expensive per bag but you will feed less. Also, every dog is an individual so metabolism will make a great deal of difference. Dogs will eat more when they are more active as well as when it is cold - it takes energy to maintain body heat.
I have a German Shepherd. I feed Victor Hi-Pro. A 40lb bag of food costs $35 and last a little over a month. If I fed Ol' Roy, I would spend less$$ per bag but he would eat more. Since there is more corn and bulk matter in the food, you will also have a larger amount of poop to clean up since so much of the food is not digestible.
I would not let the dogs fend for themselves as far as finding food. One, too great a risk of parasites = greater vet bills, shorter lifespan, etc. Second, what happens when the local prey gets low or in the winter time? The dog will be forced to either eat what he is supposed to be protecting or wander away from home to find sufficient food. Wandering from home means chance of being shot, chance of preying on livestock at neighboring farms (dogs don't see the rules as "don't eat livestock" instead, they know "this goat belongs to me, I don't eat him. But that goat next door would be delicious"). Third, insufficient diet = higher vet bills, more health problems, shorter lifespan.
There are many options for feeding dogs, including a raw diet. If you plan to process your own meat or have meat butchered regularly (especially if you also hunt or have friends who hunt), this could be an inexpensive option. It takes a bit of research beforehand to learn how to plan a balanced diet but the expense will be low if you are already aiming to be self-sufficient.
