Don't get bogged down in the details just yet - it's a long way off. The short answer is that it is of course possible...
For flight planning, the free version of SkyDemon does not show airspace outside the UK. Try to use for instance
SkyVector for some rough ideas. Click on the 'Flight Plan' and enter, for instance "egll ebos ehkd edhk ekch esgp" and see what it gives you.
With a full EASA PPL and flying aircraft similar to what you are likely to learn in (i.e. the C of A aircraft referred to), the only thing stopping you going all over Europe (or across the pond and around the world, if you wish...) is the weather and your endurance (your aircraft and your own).
Whereas the second of those can be managed with good planning, the first is more of a random element and can never be guaranteed. So, to avoid "get-there-itis", even if the trip to Göteborg can be made in a day or two, you are probably better off setting aside at least a week for the trip there and back, and treating the trip itself as an objective, and the fact that you may get there as a bonus.
Agree with WKW re having this as a longer term incentive. I have very good friends in the Netherlands and my family is in Norway. Visiting them was on my list and gave me something to aim for post PPL. Ultimately, my girlfriend is from Melbourne, Australia... just give me a bit of time and I'll get there
