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Hej!
Been there, seen that, done that. In August 2014 we moved from Amsterdam to Östersund in Jämtland.

First and foremost you'll need to get yourself a personnumber. Without it, you're pretty much screwed. You can get a personnumber by applying to Skatteverket in the nearest town. To get a personnumber the formalities are not entirely the same throughout the whole of Sweden we were told.

We needed to present a sound and locally approved business plan, proof of finances (show that we were able to support ourselves for a considerable amount of time) and proof of insurance. The latter can be a tricky one, seen as you're no longer ensured in your homecountry and you need a personnumber to be insured in Sweden. A catch-22 if ever I saw one. There is ways around that with special temporary 'expat-health-insurances'. It took about 8 weeks for all the paperwork to be finalized. We were not done by then, besides a personnumber, we needed to get a proper Swedish ID card too. You'll need to show this here there and everywhere to get stuff organized. This took another 2 weeks to get organized. This was again done through Skatteverket. By the time you'll have all the red tape organized, you'll know all the ins and outs of everything and everyone at Skatteverket believe me!

Your question about the freelance market is kinda hard to answer. Freelancing in what? And in what area of Sweden? We're based in Jämtland and we work as freelance photographers and translators. It takes a long time to get yourself established. And I don't mean just with all the paperwork and all. It took the Swedes here some time to get used to the idea of 2 foreigners working as photographers. Although everyone is friendly enough, it takes time for the people here in Jämtland to actually accept the fact that you as a foreigner also wants to join the hunt for cool assignments.

So yeah, a lot of patience and a good sense of humour, not to mention a great winter with lots of snow, help to make it a really memorable time here.

Hope this was of help to you.

Not an answer, another one with the question.  I have a business selling historical jewellery at Viking and Medieval shows (runesmith.co.uk), I've been doing it in Britain for about 30 years but for the last few summers I've covered Danish and Swedish shows with some success.  But that's been under the radar as a visitor, I'm trying to work out how much harder it will be when I have to follow all the Swedish tax rules.

For instance, a Swedish friend who does the same sort of thing full time has this year been forced by the tax office to buy an electronic till (costing about £1k) to run all her transactions through, even though she's working out in fields in the wind and rain.  I'm afraid we're not looking at the sort of sensible exceptions the UK tax office makes for small businesses.