The worms, according to Mike Johns, set up intestinal and liver problems and lower the immunity of the bird , so that secondary problems arise and the bird cannot digest food.
The bees build up a store of honey during the summer which they eat through the winter. Beekeepers will take a surplus of honey from the hive, but won't take all the honey there is. They also feed the bees with sugar syrup after taking the honey to make sure the bees have enough to see them through the winter. Honey.
The European honeybee can survive the winter, just not the africanized bees. More to the point though, honeybees aren't at all native to North America. Before they were brought here there was an abundance of native pollinators all pollinating an abundance of native plants.