The rules say "At the end of the combat phase, discard all shadow cards that were dealt this round."

Can the players do this in any order, so that the least threatening encounter card is at the top of the discard pile for quests that put such cards back into play?

Or do you have to discard them by player? First player, then second player, etc. In that case, do you discard them by order of threat like they are dealt?

It's all at once, which means you can discard them to your advantage in whatever order you choose case there are any effects which interact with the encounter discard.

Note that when an enemy is defeated its shadow is card is discarded at that time, so only shadows for enemies still in play will be discarded at the end of the phase.

Right, and when the enemy is defeated it is placed in the discard pile first and THEN the shadow effect. And cards like Armored Destrier discards shadow cards immediately while cards like Burning Brand just cancels them until they are discarded as normal.

2 hours ago, RogueSeventeen said:

Right, and when the enemy is defeated it is placed in the discard pile first and THEN the shadow effect. And cards like Armored Destrier discards shadow cards immediately while cards like Burning Brand just cancels them until they are discarded as normal.

Almost exactly right - when you defeat an enemy, you can place it and its shadow card in the discard pile in any order. But otherwise, you are correct.

Are you sure? The rulebook says " If that enemy leaves play, discard its shadow card from play." Doesn't that imply an order?