I had a 9 month old Buff O hen go broody on us in December while we were having a mild stretch of winter weather. It was like WHAT are you thinking, silly hen. It was hard for me to do as she was so determined to sit on whatever eggs she could find in the nesting boxes. Which in itself was funny to watch. If the box next to her had 4 eggs in it and she was sitting on 2 she would move over to the box with the most eggs in it and occupy.It was like she could count and knew 4 was a higher number than 2. After 4 days of arguing with her about it, she went in the broody breaker box (which really is a miracle invention that every chicken person should have) for three days and finally kicked the urge. I was glad as the next week, temps went down to single below zero digit lows for several nights.
Locally, towards the end of February, first of March, the farm stores start getting chicks in. I'm going to resist as I want broody hens to do the booding for me this spring and summer. So personally, it's up to them. As soon as the weather gets to a point where the nights stay above freezing I'll let nature take it's course.