The problem starts with the idea of peasants going off to war. Firstly, the middle ages refers to a large period of time, across a huge stretch of land, so the circumstances will vary.

Generally speaking, Bill the Cabbage Farmer isn't going to war, at least, not most of the time. Peasantry in general are not trained for battle, and are generally more useful tilling the soil. Discard at once the mental image of a feudal knight rounding up every cabbage farmer with pitchforks and leading them into battle. Without armor and shield, the average human stands no chance against even the limpest of arrows. This peasant crowd would be slaughtered, and driven off in short order in a fight, and the lord would lose out on a large amount of laborers.

Now, the common folk did have obligations to serve in the levy, but they wouldn't be able to do so without some small semblance of protection and weaponry. A spear could be furnished out of whatever metal implement available, and a shield is easily made from wood and hide. With the mandatory participation of the levy in mind, Bill the Cabbage Farmer would get these things ready before going to war. By the time a 'peasant militia' gathers, they would all have actual weapons and armor.

Source: Early Carolingian Warfare: Prelude to Empire By Bernard S. Bachrach, specifically, from the pages 55 onwards.