Considering the area you live in, I doubt it's an ACD mix -- unless ACDs are in fact common where you are? Over in this part of MN they are not. And Shibas are even more rare than ACDs here, so that's out again.

I think it's really fun to try and guess what breeds your mix is out of, but when it comes down to them looking like a "rare" (for your area) breed, the likelihood of them being mixed with that breed is slim. I can see the chow in her, definitely, and probably some Shepherd or Lab.