Blizzards would be the worst weather for the pioneers. The snow would fall heavily in the high mountain passes. The pioneers could have frozen to death. The snow would make it very hard for the wagons to travel. The wagons would just sink in the snow. It was hard for the pioneers to walk in the snow, too. They needed to wear snowshoes to get around.
The wagons didn't offer much shelter against the snow and wind. It was hard to see where they were going, too.
If the pioneers didn't have enough food when a blizzard came, it would be hard to find food in all that snow and wind.