we too had a hen go broody about 2 weeks ago, right in the middle of a cold spell.
in the summer with our 1st broody, who we kept finding in her original nest in the 1st few days of giving her eggs, i know for a fact she was off the eggs for a minimum or 4 hours in the early stages of her set and when i put her on the nest the first time, they were stone cold, all 7 of her eggs hatched.
again with the new broody she was hanging around the laying nest, a lot, and we chose some eggs for her to sit and put them where she would eventually sit them, in the 1st couple of days we had to keep putting her back on her eggs, i think initially they arent fully broody and sit on the eggs they have, to protect them while they go broody completely, unlike the 1st hen who took almost a week to return to the eggs on her own, this hen did it after 2 days, i put a barrier accross to keep her in, but since shes a bantum, she passed through the gaps, but it does act as a barrier to keep the other hens from depositing their eggs where she is sitting. she seems pretty determined to sit her eggs, and i have only seen her out about 3 times.
in the summer the broody would be outside playing sometimes for nearly 2 hrs, but it was warm then. what worries me is the fact it is so cold, i did check the eggs today when she was off them, and they did feel warm to the touch but not as warm as a newly laid egg in this weather. so all we can do is wait and see.
i wont try to say i know everything about egg development or how long they have to be sat on before they come to a stage where they can die, but a hen will lay many of her own eggs over many days before they sit them if you gave her eggs a couple of days old and she left them in the early stages, they could well be still viable, i was worried about our 1st broody and blocked her into the nursery, and let her outside and monitored her until, like i said, she went back on her own. if its possible you could lock her in with the eggs to stop her leaving them,
we have a small box fixed to the side of the nest with a small bowl of water and food, so if she wants she can feed from the nest.
if you keep returning her to the nest she will eventually learn, if not, fix a barrier up until she does.
goodluck