Since you had a chicken die I can certainly see why you have concerns. I am sorry that happened to you.
Can you tell us what temperatures you mean by cool and cold? Those terms aren’t very descriptive and it could help us respond.
My chickens get wet a lot and are not harmed by it. It’s always possible the wet and cool contributed but then again they may not have. It’s always hard to say. It’s possible there was something underlying that weakened her and she could not handle the bit of stress from wet and cool that would normally not cause a problem. Sometimes chickens die and we just don’t know why. I’ve had a couple die that I think injured themselves, one flying down from a roost and hitting a hanging feeder and one that I think was trying to get away from an amorous rooster and banged into a wall. I did not see either of these so I’m just guessing.
Do you lock them in that coop section at night or is it open? One concern is that I don’t see any ventilation. Chickens don’t need an airtight coop, that’s dangerous anytime of the year, not only in winter. The coop needs to exchange bad air for good. There are different ways to do that, to me the easiest is to have openings up high over their heads. They don’t need to be hit by a cold breeze that ruffles their feathers in winter either. Openings over their heads allows air exchange but keeps any breezes over their heads.
Part of what you are trying to do is get rid of excess humidity. Excess moisture can lead to frostbite, not death. But when their poop beaks down it forms ammonia, a lighter than air gas that can kill them. That’s a big reason why you need an opening over their heads, so that ammonia can escape. You didn’t have a strong ammonia smell when you went out there did you?
Your chickens are a lot like the wild birds that overwinter where you are. They can handle really cold temperatures if you let them. When a cold wind is blowing the wild birds seek shelter from it in trees, bushes, fence rows, some sheltered place. They have great ventilation but they can get out of the wind. They keep themselves warm by trapping tiny pockets of air in their feathers. Those pockets of air are what insulate them and keep them warm. Sometimes we make it hard for our chickens to find places out of the wind with great ventilation in our coops, but that is what they need. They do a great job of keeping themselves warm.
Wet feathers can cause problems with those air pockets so it is possible that her being wet contributed to the problem. It’s really hard to say what caused it. I never lock my chickens up because of weather and give them the option of what they want to do. I’ve never lost one to cold but I’m sure others have.
I took this picture a few years back when the outside temperature was 4 degrees above zero Fahrenheit. They can handle pretty cold temperatures.
As long as you don’t get that coop too warm and give your chickens free access to the outside regardless of weather, they will be out in cold temperatures and acclimate themselves. Heat kills a lot more chickens than cold, a lot more. You don’t want to cook them. But as long as they have acclimated themselves during the day in cold temperatures I don’t think they are going to die because of the heating pad going out at night. I also don’t believe the heating pad is necessary for them. As long as they have good ventilation and are protected from breezes they don’t need it. The main benefit would be that it makes you feel better. There is some value in that.
Once again I am sorry for your loss. I know it doesn’t help to say it but when you deal with living animals you sometimes have to deal with dead animals. Any of us that haven’t been through it yet will.