A lone bird will not suffer from the weather,
(as long as that insulated coop is also very well ventilated)
as much has it might suffer from the lack of comradery.
Your climate is pretty mild, do you even need to have a heated waterer?
Chickens are flock animals and are usually most comfortable with other birds living alongside them.
Some single birds would be fine on their own, others may not.
How long have her flock mates been gone?
How is her overall health, activity levels?
As long as she's eating, drinking, pooping well,
and is not despondent or inactive...she'll probably be just fine.
Keep in mind, that tho she may spend the long winter all alone,
she may not be overjoyed to have other birds move into her space come spring/summer.
Depending on your integration plans, experience, and space available,
it might be easier in the long run to give her away now and start with an all new flock next year.