Rather than ask which breeds are self sufficient, perhaps, more importantly, you should ask if your property could sustain chickens without input from you. If the answer to that is yes even in winter, then figure out what breed and how many your property can feed. My chickens do not travel far into tall grass. So, for me their forage area is about 3 acres and I'm trying to go clover instead of turf. My chickens love clover. At this time of year, there are few bugs. Late summer they are all over the grasshoppers.
I do cut down on the amount of feed I give my free rangers at this time of year, but, I still do feed.
Dale-Ann