Quite a few businesses have tried it over the years, a few survive, but many sadly fail. Staffing is a big issue - no staff accommodation due to non-availability or price. Poor communications and transport costs are also a big drain on businesses. You also have to factor in a short, but busy "season" for tourism, then a long season of dodgy weather and little footfall. I've seen lots of folk ponder the move to the Northern Highlands, but realised the potential problems and changed their minds. If you're young fit and healthy and have a good independent income, go for it, but if you think you'll need good healthcare or public transport - think hard about where you are based.
There are lots of second homes coming on the market - will be more in the Spring, but until we have a competent, business friendly Government at Holyrood, I would be erring on the side of caution.