Everyone had to leave at more or less the same time. Leave too early and the rivers would be full of snowmelt and the grass not high enough for fodder. Leave too late and the winter snows would fall on the Rockies or Sierras and the chances of survival would be minimal.
Remember, the wagon trains moved just a few miles a day because of the time needed to allow the animals to graze!
Timing depended on the wagon train boss, who was usually a former mountainman.