Finn here, living in Lappland.
Livin off the grid has been circeling in my mind for years and i'd say it's quite possible in finnish lappland too. Or swedish or norwegian, what ever you prefer. Gun laws and hunting will be a little problem if that's necessary, trapping might be more useful way for getting food. There's plenty of good little rivers to fish, lots of grayling and in southern lappland also a lot of pike. You'll need a car ofc and some money (you'll get income support even if homeless, so it shouldn't be a big problem) but otherwise it's totally possible. Don't go too far of some village or town, near Rovaniemi there's places where I've been wandering a lot. Last spring i broke up with my gf and lived a month beside small river here, no problem. Fishing was a bit tricky but i had a lot of dried food with me so supplements lasted quite well. Had to make a trip to get booze and cigarettes two times. It would be interesting to try that over a winter, but a cabin would be great.
National parks/wildernesses have these log huts where you could spend your time but anyone can come there whenever they want (these are on hiking trails, so people will come and go)