What part of spring? I got my first 2 batches in early June, they all laid through their first winter but didn't start until well after the older girls moulted and stopped laying until February.Most of the eggs I have at the moment are from my spring chicks. no idea why they started and stopped
I figured I would be ahead by getting chicks at the end of April. Did that twice and both times they started "on time" so I wasn't shy eggs in the fall but then they all quit for the winter! So last year I got them in early June again. All laid through last winter.
I know this isn't scientific but at least here (where I don't light the coop in the winter) it seems it is best not to get the day olds prior to June if I want winter eggs.