Temps are all over the place. We hit 86° F @2PM yesterday, and by 6AM this morning 21° F.
Yes. A 65° F drop in 16 hours.
CRAZY!
One windy, HORRIBLLY cold day I let them out and got one hen and my older Rooster (who recently became UNalived by a raptor)

frostbitten combs and wattles. I don't let them out of their semi cozy digs when it's brutal like that any more. It was a Rookie mistake.
But otherwise, its been a fairly normal February for North Central Oklahoma.
Rats? Miss Kitty catches rats regularly. (But See Below)
My "coop" is actually a chicken tractor I used to drag around daily--during the time my Bermuda Grass was green and may do so again.
When winter came, I staked it down and put up a 4 foot high Premiere 1 Electric Fence around the area, to serve as a "run". But when it's decent out, and especially if I'm around (with a rifle handy). I just let them free range.
The floor is dirt, and I spread out a little hay for bedding. I put up panels for rain and wind protection, and plan to remove them in the spring.
I've currently got 6 hens only in there, since my broken rooster is isolated. I believe it's floor is 6 X 10 feet. It's a Suskovich style Chicken tractor, except enclosed.
I have seen mice in there, several times. As stated, Miss Kitty catches Rats, BUT... when I've observed her hunting, it isn't around the coop. And she has access to the coop anyways, when they're out free ranging....just not at night. I don't 100% trust her not to suddenly decide a hen looks yummy, although they're all adults @ one year old next Sunday. Miss Kitty doesn't show sighs of aggression with my birds. (Nor does my 89# GoldenDoodle, Mr Hobbs.)
She's an outdoor only cat that adopted us about 3 years ago.
But I'd DEFINITELY NOT rule out a rat getting in my coop. It's a dirt floor after all. And Mice, yes. For sure.