How cold is cold? I will be giving my broody hen some eggs to hatch even though she will also be a first time broody but our winters are very mild here, for example the next few weeks I'm seeing lows in the 40s and highs in the 60s though it does occasionally drop into the teens, but I have seen where people have broody hens that successfully raise chicks even when the highs are in the 30s where they are. A good broody hen will care for her chicks and keep them warm even on the coldest nights but an untested broody is just that, untested. If it's really cold where you are I would probably keep my broody in an draft free broody pen to basically help her to keep the chicks warm.
I seem to have the broodiest bunch of hens in my flock because I had several go broody last year and one thing I will say is that all broody hens will more readily accept eggs, than newly hatched chicks. Even if you give her the eggs on day 18 and let her basically do lockdown she will be more likely to accept the chicks when they hatch, but I know that's not always possible, so I would be sure to sneak the chicks under her after dark. Wait until it has been dark out for at least an hour and gently place the chicks under her wings. I typically watch for a moment to see how she handles the situation and I check back several times (without actually disturbing her but just making sure she isn't being aggressive toward the chicks).
Good luck! Keep us updated!