If a player activates an ability that allows all players to gain a card, but there are fewer cards in the display than players, not all players will have the opportunity to gain a face-up card. However, players may still draw from the deck if the ability allows it.

This is explicitly stated in the rulebook under "ABILITY ACTIVATION SEQUENCING":

• "Note that dragons and cave cards are not refilled into the card display board until the end of the current turn, after all players have had the opportunity to activate the ability. This means that in some circumstances, if an 'all players gain a card' ability is triggered, not all players will have the opportunity to gain a face-up card (though they may still draw from the deck)."

Summary

• Players gain cards in clockwise order starting with the active player.
• If there are fewer cards in the display than players, some players may not be able to select a face-up card.
• If the ability allows drawing from the deck, players may still draw a card from the top of the deck.

Source: Page 11, "ABILITY ACTIVATION SEQUENCING"

Source: Wyrmspan Rulebook (pp. 10, 11, 14, 2)