"In general" is key (and in general people will get *very* mad at you if you offroad on public lands or on private land without permission - me among them). However it's perfectly legal on private land if you have permission. On my land, for example, I sometimes *have* to offroad to haul things around (supplies for fences, trees to plant, manure for soil restoration, etc); I don't have roads that go everywhere, and nor do I want them.
There are three cases on public lands where people won't get mad at you offroading. One is if you're in a björgunarsveit (rescue squad) - they go wherever the heck they need to if there's a person there. The second is up on the glaciers, as those get wiped fresh every year. The third is, in specific locations, there's areas specifically designed for offroading (including difficult rock crawling).
It should also be mentioned that some of our highland roads are worse than what people in most countries would call "offroading" ;) Where they cross lava fields, for example, you'd be crazy to go over them at more than 15kph/10mph, and even that can be pretty jarring in places. But they don't involve any serious rock crawlimg, they're designed to be such that any high-clearance 4x4 can get through (don't even think about it with a regular passenger car, though!)