So this question came up during playtesting last night.
One player has no cards in hand and the other player has 2 cards. The player with 2 cards reveals Threat from the East and chooses discard. Does he still discard the 2 cards in his hand? His argument was that he didn't since he couldn't successfully do the 3 cards it asks for. I argued that you would still have to try to fulfill it even if you can't. Similar to an effect that would have you draw 3 cards even if you have already drawn 2 outside the draw phase, you would still try to draw and then stop once you hit the draw cap barrier.
Relevant card text:
Threat from the East
When revealed, you choose one:
Each player draws 3 cards and then discards 3 random cards from hand.
Each player discards 3 random cards from hand then draws 3 cards.