How old she? What is her behavior like? Her eating and drinking? Her breathing? Is poop normal? Did you check her for injuries? Bites?
The cold feel plus color change seems more to indicate a circulation problem, rather than only a problem in uptaking oxygen. This could be a heart problem like congestive heart failure, or something interferring with her circulation like a blood clot.... Does this happen with mites?
I would isolate her and keep her rested and calm until you figure it out or it resolves itself.
I have seen this before in some of the bigger breeds. I've had Plymouth Rocks and Jersey Giants whose combs did this, and my Delaware rooster (he is a big 9.95 lb boy) has a comb that still turns part purple sometimes, for reasons unknown, eventually fading back to normal. I would bet on a circulatory issue, but that may be applying mammalian logic to a bird system for all I know. With Hurley, I just keep an eye on him when I see his comb's gone purple, make sure he's still moving around and acting normally. I think that's the bigger health indicator most of the time. So, in short, I'm not sure why your hen has a purplish comb, but I've had many with them, and they've all lived normal lives. Hurley himself will be 5 or 6 this year, depending on who you ask.