Private rallying...

[needmorespeed]

If you have an Impreza, could you take it on a track in the forest and expect it to do okay?

Are there any private off/dirtroad tracks in Europe that allow you to bring your own car and just have some fun with it?

[shurik]

If you lucky enough, you can expect it'd be okay, but depending on track and probable mistakes you may end up with ruined toe-in, camber, bent links, sway bar, not talking about ammos or springs. And all this stuff will take fair amount of money out of your pocket.
Keep in mind though, that it's not that hard to roll a car, even if it's an Impreza, so think about installing at least a road use rear cage or a bolt-in rollcage. It may save your life.