Apparently someone had cleared much of the snow from around the car the day before. That made things a lot easier. The tow driver hooked a chain around the frame and used an electric winch to slowly haul it up out of the muck. The right rear wheel was stuck nearly 6 inches deep in mud. He towed the car to the nearest Chevy dealer, Copple Chevrolet, to thaw out the engine compartment and diagnose some problems.
My SO had been complaining about the engine running rough, and I suspected the spark plugs. It had been a good 35-40K since they were last replaced, so they were well overdue. He was freaking out afraid it was going to be something horribly expensive.
Sure enough, it turned out the only problem with the car was it needed a tune-up: new plugs, plug wires, distributor cap and rotor, PCV valve and fuel filter. I got the car back this afternoon and took it for a test drive. It seems to run perfectly now.
I asked for the old parts (per Animale's request), and I examined the plugs. One of them had electrodes that were completely black. Well there's your problem!
I noticed a problem with the bill, they charged $21.68 for EACH of the 8 spark plugs. I could understand if these were some special plugs, made of some exotic alloy or something, but these are plain old Delco CR34TS plugs, which run about $2.00 at most auto parts shops. It has to be a math error. Maybe the $21.68 was supposed to be for all 8 plugs. They couldn't possibly think they could get away with charging $173 for $16 worth of plugs.
EDIT: I Googled the part number, and it's for a pack of 8 plugs. They billed me for 8 packs of 8 plugs. Whoops!