Once you get past the juvenile molts age does not determine when they molt. The cold doesn't either. The main trigger is the days getting shorter. When they were feral the cycle was to lay eggs and hatch chicks in the good weather months, stop laying and use the nutrition they found to grow new feathers instead of making eggs in the fall, and wait until the weather and food supply got better in the spring to start laying eggs and hatching chicks. We've changed them some by domesticating them but the basic pattern holds for most chickens. I'm talking about our backyard chickens, not the commercial ones where lighting and feed is tightly controlled. They also use adjusting the lighting to force a molt.
It is possible some or all of your chicks will not start laying until the days start getting longer in the spring. It is also possible some or all of your chicks will start laying this winter when they get old enough and continue laying until the days get shorter next fall. You don't get guarantees with any of this.
To show you how confusing and uncertain it is, I had three pullets that hatched in early spring. None of them laid until nine months later. The first week of December, one of the shortest times of the year. Two of them started laying within a week of each other. The third did not lay for another two months, she waited for the longer days of spring. What is really weird is that I hatched some of their eggs and raised pullets. Most of those pullets were laying before 24 weeks of age, not nine months.
Some people on this forum would have you believe that every pullet starts laying at the same time, regardless of circumstances. Not in my world. I expect an egg when I see an egg. Until then it is just hope.
Good luck and welcome to a wacky adventure.