With stovetop cooking, is there a way to retain heat but let moisture escape?

You don't really have much control, at least not very directly like turning a knob. You can control it a bit by your choice of cookware - a thin-walled pot which is relatively high in comparison to its width will dissipate heat more than a squat, thick-walled one of some non-conductive material like cast iron or ceramics. If you want more moisture escaping, go for wide vessels and don't heap your food in them, place it in a single layer.

Another option is to cook food in an oven, which allows it to be heated slowly, but the moisture is not as trapped as it would be in a closed pot, so the food doesn't become soggy.

Your examples here are not generally tackled by separate moisture/heat control, though. For the mulled wine, anything that escapes with the lid off will also escape with the lid on. People usually simply reduce the temperature and keep the lid on, to save energy, but keeping it with the lid off doesn't make a difference. For the onions, if you want them done quickly, you shouldn't be making them in the slow cooker at all, but shallow frying them in a pan. I know you said these are examples for illustration, but I suppose that for any other examples you might come up with, there are already established ways to do them and your problem might be arising from not following those.