Sorry to hear Millie was hurt in the fight. Honestly, I wouldn't worry too much about being off the food for the first day, it could be the meds if she's on any, or from when they probably medicated her to stitch her. Of course, no food in, no poop out. If she doesn't eat her food tomorrow I would try to offer her something easy to eat like boiled hamburger or chicken with some steamed rice. It would be easy on her tummy and probably very tempting. Just don't let her gorge. As for being cold - she probably is not. If she is used to being outside her one leg is not going to make a huge difference. Will she have access to the heated barn still? If so, don't fret. I know it's hard not to. Not putting the cover on the leg was a good idea, she could have pulled stitches if she tried to remove it. Does she have a cone so she can't lick at the stitches?
Good luck to you both. What type of dog is Millie?