From the outset, they were able to manage their relationships with the EU through joint agreements established over MANY, MANY years. Swiss infrastructure had not been destroyed by WWII, so its post-war situation was never as dire as in the rest of Europe.
The EU (in its earlier incarnations) did just fine without Britain for about 20 years. It will do just fine without it again. But Britain now has to start from scratch. THAT will not be easy.
Britain already had a special status in the EU. It was not part of the Eurozone and not part of Schengen. It got to receive ALL the benefits, but was less affected by the disruptions. In other words, it had its cake and could eat it too. With Brexit, it will be left only with crumbs.
Brexit is not a good outcome. It is also NOT the outcome that the Scots, the Northern Irish and Londoners voted for. Thus, this Brexit being about the "will of the people" is not quite accurate; it is about the will of the people in some regions - generally those less developed.
Scotland will break away now and Northern Ireland will perhaps unite with the Republic in some form so that both entities can stay in/rejoin the EU. This leaves England (with an unhappy London) and Wales standing all alone, like the cheese in the nursery rhyme.
Oh, and I live in Switzerland for the most part. 
I am very sorry that the UK voted this way.
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