how negative can a bad O2 be?

my car is throwing a code for a precat O2, has zero power if its cold outside.... like could be passed by a bicycle.



heres a few reasons I ask,

for the first 2-3 minutes the car is running (regardless of temp) it runs like a champ, all the power I would expect from a 323i engine (from what I understand the Ecu is in a closed loop fuel map for the first few minutes and doesnt use input data from sensors)



once the temp reaches operation (center of guage) the vehicle is still sluggish, untill approx 3/4 throttle is applied, then all bogging seizes and the car begins to accelerate at a very healthy rate



also, O2 sensors rely on temperature to function correctly. hence the horrible performance when cold, and i have also noticed. when driving the car in cold weather it gets terrible efficency, like 16mpg but 20mpg (city) on warm days, and if i drive a short distance and dont let the veh reach its desired temp, the exhaust is very, very rich..... i could almost light it with a lighter.



i have new vanos seals, solenoids, intake CPS, VCG, CCV and hoses, all new vacuum lines, and intake gasket.

(I was originally blaming the bogging on intake leak)