I don't think it's entirely silly to have a tree/presents for the outside... but only because I've seen it done IRL plenty of times. (May sound strange if you've never seen it, but some people who do "extreme yard decoration" for Xmas put what's essentially a public yard replica of your typical indoor tree setup outside. It's just another pretty thing to be lit up on the yard. As for the presents bit, they're empty boxes, of course!)

However, I do agree that there NEEDED to be a tree for the indoors. It's ridiculous that there isn't one, and little to no good excuse for why they didn't put one in the game.