Personally I wouldn't let my hens try to hatch anything now, but that is only my opinion. If you have a hybrid who lays all year round her cycle is a bit messed up anyways and she doesn't know it's not a good time of year. If you are just having an unusual cold snap though and live in the deep south and it's going to be mild soon maybe it's different. Our hybrids layed all year round with just a short break but our purebreeds quit for the winter.
Our hens, or at least a couple of them, are forever going broody in the summer. We let one of our bantams sit on some eggs in the summer of 07. It was a very cool and wet summer, and this affected the incubation time - they went much longer. I was sure they were all duds or had died in shell. Banties take even less time than regular hens but she went 25 days!!! I just knew we were going to have stinky exploding eggs very soon! But after coming home from church on the very day I was going to dispose of the eggs, we saw new baby chicks! So I was wrong to give up on them even though they went a week over what they should have done which is a long time when you are dealing with dead eggs which might explode. And the babies were gorgeous Partridge Pekin (Cochin) bantams.
As a previous poster said, you'll want to have the chicks in a flat zone - so they don't have to step up into the house to be with mom. We used a rabbit hutch and my husband cut a floor mat and tacked it onto the front of the hutch so it made a ramp all the way across for the chickies to walk up on. It was only a rise of 1" or 1 1/2" but that is still too high for them to step up to.
It was a very fun experience, great for learning. I learned that mother hens have different calls depending on the circumstances. Like, "lookie here, this is good to eat, come get some!" or "Danger! Come to me!" and "Danger! Don't come to me, but stay hidden!" Amazing.
We were advised to keep mama and babies away from the other hens for a while - to where they can see each other but the other hens can't attack the babies. Mother hen can't protect all the chicks at once if there are many chicks and many other hens in a close environment. (someone with a bigger property may not have that problem) When we let them out of their run at first, for a few minutes at a time, we stayed right there, and built up the time they were out with their mother outside of their run. Eventually when the babies were big enough the mother began going back to the main chicken house to sleep, leaving the chicks (now really pullets) on their own. She began chasing them off if they came too near her.
And another thing - since mama and babies will be on the ground, besides keeping them safe from the other hens you will want to make sure it is predator-proof as possible. I was advised to move the mother before we got the real eggs to hatch, to her new place and see if it put her off setting. Some hens, when they are moved to the broody coop, lose their broodiness and it is better to find out this while you are using dummy eggs instead of real eggs.
I hope if you do it that everything goes well.