The first thing I have to say is that it feels like the collider on the player is too large. In the original, there isn't much danger of turning into a tree which you've visually passed, only colliding head on and it can be frustrating to try to weave in and out of trees only to hit one.
Additionally, there seem to be a few things about the tree spawning which could be improved. Once I had a tree spawn directly in front of my with no way to avoid it. Additionally, the density of the trees seems to change a lot ocassionally making it very difficult to move.
Overall, the controls feel good and the way you handled the endless space works well enough.