I'd be hesitant to make too many drastic decisions about which ones to keep or not keep this time of year due to potential reduced laying from molts, short hours of daylight, and such, but egg laying is an inherited trait from both parents. The rooster wil contribute to these traits also.
If you hatch eggs from chickens that lay a lot, their offspring tend to lay a lot. If you hatch eggs from chickens that lay well in the winter, the offspring tend to lay better in the winter. This applies to the overall flock tendencies, not necessarily to one individual hen. You never know what genes an individual hen will inherit, so this may not apply to one specific individual hen. But if you hatch enough chicks for averages to mean much, yes chickens tend to produce offspring that have their traits.