Ain't nothing wrong with dry dog food as emergency rations. Since your chickens free range it's not like they are starving. But if the natural food source is scarce, it doesn't hurt to supplement with a 'novel protein source' which is a fancy way of saying feed what you have. I'm not sure what part of the world you are in, and I'm too lazy to look and see, but snow does challenge foraging chickens.
If you want to ease your feed bill, you'll have to get out there and do some fancy talking. Check out your local feed store and see what they do with broken bags of seed. I recently got lucky when I was checking out a local, family owned feed store, and saw some torn bags of wild bird seed. I asked if they would sell the bags at a cheaper price. At first they said no as the feed company would reimburse them. After further discussion I discovered all the seed company needed was an empty bag of seed as proof for rembursement, so I haggled a price if I supplied my own bags. I got a sweet deal and feed the wild bird seed as a treat for my hens.
We are all familiar with feeding chickens on a limited budget. You can feed cooked beans. Some stores sell 20 lb bags of uncooked beans, and if you you don't mind doing the cooking, cooked beans are a good food source.
Around here we have those tiny Flower Bakery stores that sell day old bread. Catch those folks on the right day, an you might be able to dicker a deal on out-of -date bread. Or you might score on torn bags and go home with a trunk full of bread you can freeze.
I hope these suggestions help you out. In these times it doesn't hurt to think outside of the box. You'll have to get out there and learn to wheel and deal. And while I'm too lazy to look up your location, when it comes to my animals, I ain't lazy at all.
