If I own my own business/am freelance, can I work anywhere abroad?

What you describe sounds like the situation that most of us would like to live in, touring teh world and working from our laptop. I have no doubt that some people do this, but I also suspect that they are very rare indeed. There are computer jobs that could be done anywhere, such as computer programming, or even a data controller, or trading Forex online are just some of the jobs that would also allow you to work in any country. In any of these jobs, if you are making enough money you could in theory work from anywhere that your income would support you to enable you to live. In some of these jobs, you might be able to get away with travelling purely as a "tourist" and thus not need a visa, especially here in the UK where the authorities are seemingly hopeless at tracking down immigrants who overstay their visa.