Months ago a thread was posted about 5100's running lean. I mentioned in the thread that my dealer [D&D enterprises-Salem Indiana] cut a notch in the rubber gasket under the air filter. This foam gasket makes the atmosphere side of the diaphragm pull air through the air filter. Dealer says plugged air filter equals not enough fuel pumped to carb equals burnt up saw. I don't know if this is true or not but my saw is still running fine.
I did have to have the coil replaced.
A plugged air filter doesn't equal a lean saw. The fuel diaphragm is pumped by the case pressure. A dirty filter equals a rich running saw because there is more fuel than air.
It sounds like this saw has been run lean. 6 months of weather makes a huge difference in saw tuning. Since it is now cold, air is more dense. The colder it is, the more fuel you can add. So if this saw was set up when it was 70 degrees (lean from the factory to boot) and hasn't been adjusted at all since then, this cold weather may push it over the limit in terms of a leaned out air/gas mix.