Hmm...
It seemed to be interesting at first, but it soon became much too slow. In most snake games, you "die" if you crash into a wall. However, in Snake Forest, you simply teleport to the other side of the screen. Not only is this the exact opposite of the Snake idea, it makes the gameplay extremely long and tedious.
I realize that, eventually, you become long enough that it becomes more and more difficult to avoid your tail. However, without having to worry about any walls, the pressure goes _way_ down. A player can very easily just teleport to the other edge, turn, etc, etc, etc, until they get to where they want to go. If played correctly (no pun intended), the chance of death is almost nil.
Perhaps you could make the speed increase more drastically. Also, you might make it so that there is health and the meter drops if you don't get food in time. I haven't seen this in any Snake game, and I think it would make a _wonderful_ and _welcome_ change to the classic Snake. Also, it would make it less appealing to run away from yourself to line up the perfect shot -- you'd have to go for it ASAP! Finally, add in some trees that you need to avoid. This would add to the stress by making us avoid both our tail and random trees as well. It is, after all, a forest!