It depends. Winter worker bees live several months. Summer worker bees live only a few weeks. (I'm referring to honeybees here, not other types of bees.)
Winter bees have to live longer because the colony has to "hibernate" through the cold winter months, doing nothing but keeping warm, then in the spring it needs enough bees to reboot the cycle. On the other hand winter bees don't have to forage. Summer bees live less because a) they don't fatten up, b) they fly a lot.
It depends as much on weather as on forage availability. If there's no nectar flow during the winter, then they'll just not spend so much effort on foraging, maybe? I'm not sure. Where I am it's hot much of the year, but winters are not a walk in the park for the bees, so they definitely hibernate. (They don't sleep all winter, just they don't go out on cold days, but since it's Texas there are sufficiently warm winter days they will go out on those days, mainly to poop.)
San Diego native here. California bees are incredibly docile and produce honey year-round. They produce more slowly in the winter due to availability but they don't hunker down+expel male drones like in harsher climates.
If you take a California queen to a state like CO they tend to do poorly the first year. They're not used to things like other hives raiding honey stores in winter. It's pretty fascinating!
Winter bees have to live longer because the colony has to "hibernate" through the cold winter months, doing nothing but keeping warm, then in the spring it needs enough bees to reboot the cycle. On the other hand winter bees don't have to forage. Summer bees live less because a) they don't fatten up, b) they fly a lot.