What are the white trees?

This page might help you.

There are some secrets to discover, as well. For some levels, if you manage to make your tree tall enough to reach the dark blue flower, it will bloom blue flowers and you’ll get a few blue stars added to the sky in that level. The level icon will also show a blue star. Some levels don’t show a blue flower, but you can get them anyway. The trick is too look for the shooting stars. It’s a nice little bonus to go back for after completing the game. I even found a little white sapling when I went back to one of my blue levels. Not every level can turn blue, though. You can track your progress based on the stars in the sky in the level select screens.

My guess is they're just little easter eggs for getting the blue flowers. Apparently if you grow your tree into them white flowers grow around the sapling.

The stars in the menu connect every time you get a blue flower, to complete the constellation of a tree