Welcome to EM!
Air from the outside could be getting into the exhaust system somehwere - check to see if there are any rust holes anywhere near the O2 sensor in your exhaust manifold/pipe. Also check for loose connections between any of these pipes that would let outside air in. I've had this problem on every car I've owned to date probably because of the salty roads in wintertime. I just end up needing to replace the long central exhaust pipe that extends between the catalytic converter and the muffler.
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