I think if you had a charging problem, you'd see different lights - either the charging light or, well, all of them.
Does your car idle okay when you first start it? If the revs bounce or lope at all, you might have a problem that's worth having a shop look at.
But if your car idles just fine, your symptoms wouldn't concern me at all, considering your driving habits and climate. If there's a significant temperature difference between the time you park it and the time you drive it again, you can see the CE light come on. Since yours only comes on while the car idles, I suspect that's the issue.
But I could be completely full of it.