DIY'ers tend to just throw parts at things. We've all done it.
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My favorite gimmick is Autozone offering to pull the codes on a car for free. Well as you know a code reader doesn't say, "replace this part". I had a friend with a check engine light go down there. They said you need a knock sensor it's $168. He calls me and says they want to sell him a knock sensor. I told him if those people could fix anything on a car they'd be working as a mechanic not retail for minimum wage. Anyway, it was just old gas, the knock sensor was working as designed.
I agree with your and at least on other poster's recommendation based on the following:
IF we apply logic to what limited information we have about this problem. It only idles strangely in cold weather.
So…..
It is not a cold start injector since they don't have one.
It is not fuel pressure, not temperature effected.
It is not the ignition system, it would run better cold if anything.
It is not a dead short, wouldn't go away with warmer weather.
It is not a bad ground, would get worse with heat not better.
It is not an open circuit, it would not get better with temperature.
The throttle body is undoubtedly dirty and in need of cleaning, but would probably not cause this specific problem.
The IAC is the logical place to start. If we can all agree on that we can move forward.