My test to see if a hen is broody enough to deserve eggs is that she has to spend two consecutive nights on the nest instead of in her normal sleeping location. There are several things that indicate she might be broody but I've had hens do all of those and not really deserve eggs. Someday that test may fail me but it hasn't yet.
As far as winter brooding you might find this thread interesting. It's the best documented winter hatching I've seen.
http://www.backyardchickens.com/t/947046/broody-in-michigan-winter
Some people worry if it's the hens first time being broody. I don't. I've had great success with first time broody hens, even young ones. I've had problems with broody hens the second time around when they did great the first time. If you really want a broody to hatch chicks and raise them I would not let that stop me.
I've seen a hen get her chicks out of a 10' high hay loft. She said jump and they did, bounced up, and ran to her. I've had them hatch in nests four feet off of the coop floor. One of those is in the photo below, the white one. That is a cat litter bucket that did give me a problem. The top was 7-1/2" x 11-1/2", the broody hen was sitting too close to the edge because of the size. When they hatch chicks often climb up on top of the hen while waiting for the later ones to hatch. Usually that's not a problem but in that nest the hen was so close to the edge that they missed the nest when they fell off of her. Four different times I picked a chick up off of the coop floor and put it back in the nest with her, probably the same chick for most of those. It fell four feet and did not get hurt. A relatively high nest doesn't bother me but a nest that is too small does.
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I've never had a problem with a chick not leaving the nest when the hen told it to. If I did I'd most likely just pick it up and set it on the coop floor so it could go to the hen.
After they bring the chicks off of the nest mine never go back to the nest. I do not have any nests at ground level, my broody hens just take their chicks to bed on the coop floor. The first night or two it could be out in the middle but it usually doesn't take them long to figure out a corner is out of the way.
Some of us let our broody hens incubate, hatch, and raise the chicks with the flock. Others may isolate the broody for any of those stages. As mentioned above the eggs need to all start incubation at the same time. And you don't want any new eggs to show up in her nest. If you decide to let her hatch with the flock let us know, we can give more detailed suggestions. A photo of her nest could be very helpful.
If you decide to isolate her let us know that also. If you isolate her she needs to be locked with her nest, food, water, and a little room to go poop. It doesn't take a lot of room but she needs a bit. By instinct she should know to not poop in her nest and foul her eggs but she doesn't know that about food and water. You may be cleaning those out. Just let us know. Some people use a totally separated pen; some might fence off her nest in the coop. There are always different ways to do these things.
I've never put food or water near my broody hens. As they hatch with the flock they have the same access to food and water the rest do. I've seen a broody hen leave her nest for about 15 minutes once a day for her daily constitutional (food, water, poop). I had a hen that left her nest twice a day for over an hour each time. Some I never see off of her nest but I know she's coming off because she is not pooping in her nest. Each one is different in how they do it.
If she is truly broody and you break her from being broody there is an excellent chance that she will go broody again later. But that is just a chance, not a guarantee. And there is nothing that says it will be any more convenient to you if she does.