Out favorite answer here on r/AskHistorians is, "It Depends." Sometimes looting and foraging was a systematic practice overseen by the higher-ups in a military organization. Other times, it was a messy free-for-all.

Just one point of order: It is a common misconception that pre-modern armies consisted of "peasants." By and large, people who owned arms and armor either owned enough property to be able to afford the paraphernalia necessary for soldiering, or at the very least were well-connected enough to have become a dependent attached to someone willing to arm them.

Even in the armies of the Italian City-States between the eleventh and thirteenth/fourteenth century, by and large the wealthier citizens were the ones being called up for military service. In fact, it was only in the moments of greatest desperation, like during the battle of Monte Porzio or the Battle of Legnano during Emperor Barbarossa's descent into Italy, that you see situations where the wealthier members of society are called to provide arms for the urban poor. You do often see situations where the more well-drilled and experienced members of an aristocrat's armed retinue (his Serjeants) are charged with keeping order and discipline amongst the "rabble" of urban levees, however that's more a product of the fact that regardless of class, urban dwellers generally wouldn't of had much experience soldiering.