the service engine light goes on and the engine runs rough in cooler weather

See my reply to vibration at speeds 40-50 serv. eng. light on. On page 1. This symptom happened to me but I got it still running good enough to commute to work everyday. Still some vibration but Not as bad as it was. Now my car just dips down to under 500 rpms at stops. These are usually Calif. emission spec cars which means they are very finicky. I had to replace both cat converters at 170,000 miles even though I tried to avoid it. Took other measures first. Then I and mechanic both agreed the converters were gone as the material inside rattled if you slapped it. O2 sensors may be going bad but you can fix yourself if you order the sensors yourself online it is cheaper. See previous answer I referred to!