Best Way to Winterize a Chainsaw?
This is one of those questions that elicits much gnashing of teeth, along with oil change interval and 87 octane vs. "premium". It comes down to opinion and the various factors:


Length of storage (weeks, months, longer)
Engine type (two-stroke vs. four, cylinder wall linings, carb type, etc.)
Climate (humidity, temperature)
Oil and fuel types


Running a two-stroke engine dry means depriving it of lubrication, if only for a few seconds. I'm not sure how effective residual lubrication is, and that probably depends on the oil type. 

So, I personally like a hybrid program of sorts. I stabilize my fuel, and I run my machines every month or 6 weeks to normal operating temperature. This way they stay lubricated, the carburetor circuits don't dry out, and I don't run them without lubricant.