O2 Sensor

[stublejumper]

Hello I am a new member and i hope some one can help me.I live in Canada and when its cold out -30 + i throw an o2 code i have replaced all the sensors and still they only last a week and then they are full of carbon.I have changed the thermosat and that has not helped the dealership has not been any help ether i was thinking about cutting the cats out and reprograming the ecm ($800 bucks) need help.2004 gmc sle 80 000km 4x4 stock engine

[stublejumper]

Just wondering if you guys have any idea why i am making so much carbon and fowling 02 sensors the truck runs great for about a week until the sensor gets coated it looks think a black cuet tip thanks for any help