In a nuclear battlefield, the concentration of forces into a spearhead would present a perfect target for the employment of tactical nuclear weapons. A single well-placed weapon could break up the attacking forces before they even had time to properly prepare, causing enough casualties to make them ineffective even in the defence.
This is the type of equipment it was expected an infantryman attacking an irradiated zone might need to push forwards after the employment of a tactical nuke on an enemy formation.
https://taskandpurpose.com/tech-tactics/army-soldier-future-1959-video/
Jeep mounted Davy Crockett tactical nuke:
Also we’d just fought in Korea which had lots of cold weather combat. You might appreciate those nylon layers in the cold.