1999 Jetta check engine light question

I have a 1999 (new body style) Jetta I just had a quick question about my check engine light. It was extremely cold here a few days ago, and I don't think I let the car warm up enough before I took off. As such, the car ran a little rough at first, and the check engine light came on. I stopped, let the car idle for a bit, and since then (2 days ago) the car has run perfectly fine - but the check engine light is still on. I'm planning on taking it to get the codes read, but my question is this: Does the check engine light remaining on mean there could still be a problem? Or does the light remain on after an error code is stored (at least until the code is cleared)?

The reason that I ask the question is that the check engine light seemed to come on because of a specific event (starting when too cold). Since it runs perfectly normally now - my first thought is to get the code read / cleared, and see if the light comes back on. Does this sound reasonable?

or maybe 100 or so other reason that can turn a mile light on. That's why you need to post the fault codes, and I bet it's not the O2 sensors. "the car ran a little rough at first"... my money is you have a few misfire faults and if that's the case the MIL will turn itself off in a few more days.

I'd wait a little longer and see if it clears. If it ran rough the system probably just detected a misfire and when it's "happy" that the misfire is a random thing and not a constant recurring item it might go out.

Sometimes I have observed this if the car sat unused for a long time. I haven't been able to reliably reproduce it because it happens under those conditions only, for instance after such a period of non-use, the car will not idle smoothly or idles at a higher rpm than normal until the condition clears.

The light generally has to do with an emissions failure/warning and will clear itself if the car is started without that condition recurring a few times (might last a few days).

If the problem is recurring however this definitely requires attention.