Mike P - I'm basically in agreement with Jeremiah and Gerry. I'm really leaning towards this being a valve problem, and hopefully just an adjustment problem. You'll have to study either the Kohler or CC Engine manual on how to adjust the valves. And since I suspect you've never checked and adjusted the valves on this engine before you're gonnna need a breather kit (which will come with a couple gaskets, funky mesh filter, rubber spacer). You have to remove the breather cover so you can check the valve clearances. Now, it's your choice here but if it were me besides checking and adjusting the valves I'd also pull the head, de-carbon the piston surface and head, get a good look at your cylinder walls, and replace the head gasket. I know you said the previous owner replaced the head gasket, but what caused the head gasket to blow in the first place? Did it blow because the valves were out of adjustment and now you're encountering the same problem. Do you know if he de-carboned the head when he replaced the gasket? Did he torque, run the engine, and then re-torque the head bolts? If I were you I'd be alot more comfortable knowing what the inside of the cylinder and head looked like, especially if the valve adjustments are off. I have always considered a good tuneup on these Kohlers to include replacing points, condensor, spark plug, checking and adjusting the valve clearances, and de-carboning the head and piston. Kohler recommends the head decarboning every 500 hours (which is probably every 5 to 10 years for most people). I don't know their recommendation on the other items but I would think at least that often. I'm sure hopeful that adjusting your valves will resolve the problem but I'd just like to know your cylinder and head are good, and that backfiring hasn't blown the head gasket.
Dan G - if I were you and had that dream, I'd be running around trying to find another CC unit to have on the ready all the time, just in case it does snow.
Jeff B - sure looks like cross hatching to me since the marks appear to be quite evenly spaced and repeat in the same spots as you look down the cylinder wall. And I believe not being able to feel them with your nail is a good thing. Now, I don't like that carbon on the top of the cylinder wall. I can't see the top of the piston but if the carbon is built up in the same area it will start wearing away your piston and eventually fail. So I'd definitely make sure you get all the carbon cleaned off from the top of the cylinder wall, top fo the piston, and in the area of the valves, etc.