It really hurts to lose a chicken like this. Sometimes we just don't have the time necessary to try to figure out what's making a chicken sick. But quite often, the sickest chickens, even those with scary symptoms like paralysis and imbalance and being unconscious are suffering from things such as not having eaten enough calories and being exposed to very cold temps, and these are easily fixed with just a little sugar water to revive them. From there, you can take measures to feed them and put weight back on them so they can then handle the bitter cold nights.
When hens go broody, unless we wish them to incubate and hatch eggs, we break them in the first two or three days of being broody to spare their bodies the starvation that broodies suffer over the many weeks they are sitting in a nest instead of eating regularly. It's done with a cage with an open mesh bottom so air can circulate under them and to deprive them of a nest to sit in which prolongs their broody hormones. This disrupts the broody hormones, and in just a couple days, they are back to normal and no longer broody.
Chickens handle below freezing temps just fine as long as they're consuming calories to produce body heat. Broodies normally do not consume many calories. If you want to move a chicken back outside after being indoors for a few weeks, you need to gradually get them used to cold temps again before putting them outside and be sure they're eating enough calories to produce body heat.
The respiratory symptoms may have been from an infection, but they could also have been from the hypothermia shutting down her bodily functions. If you suspect she had a more serious disease such as Marek's, it would be a very good idea to contact your state animal testing lab and see about getting a necropsy. Refrigerate the body while you explore this.