If you quit the game, any unopen Holiday Gifts you have will disappear. This does not happen on the PC, PlayStation, nor Xbox.
Diablo 3 - Switch Bug with Holiday Gifts - YouTube
As demonstrated in the video, I initially change characters, which will save the game. Also, quitting the game typically also saves the state. But changing characters, the Holiday Gifts are still there. This only happens when you quit the game completely with Holiday Gifts in your inventory.