You can activate the effect of "Trishula, Dragon of the Ice Barrier" even if there are no cards in the Graveyard, or no cards on the field, or no cards in the hand. In this case, you can still remove from play one card from each of the places that still contain cards.
The card removed from play from the hand by the effect of "Trishula, Dragon of the Ice Barrier" is chosen randomly. You do not get to check your opponent's hand when the effect resolves. However, after the effect resolves, you can check which card was removed from play.
↑Konami Judge Program Rulings are considered unverified, as their source(s) are not publicly viewable. They are not confirmed as applicable to the TCG until they have been officially published by Konami.