Sure, but there were also religious taboos to do with the dead and battle fields. One common practice was to set up a tropaion/trophaeum (ie, a trophy) to mark the turning point in battle (τροπή: turn). You can see a lot of images of these, particularly on roman coins and arches. They're basically a scarecrow decorated with captured weapons and armor.

The Greeks commonly dedicated captured weapons and armor in temples, the Romans did too (particularly after parading it through the city). There's not much record to account for whether poor soldiers would re-arm themselves or take the gear of fallen comrades, though it's probably worth noting that the ancients did believe in ghosts and angry young men killed in their prime were considered pretty much the most likely candidates to get their haunt on, so I imagine their would be some reluctance to take their stuff.