Yes, I can do the mist in post. But there are other techniques. In THE CURSE OF THE WHERE-RABBIT I believe they used a smoke machine for some shots. They shot an empty scene (no characters) with smoke and after that they shot the scene with stopmo-characters (and no smoke). This is composited and somehow it all fits together.

If someone has experience with this I hope he/she could give me a few pointers. If not, I will be happy to give the pointers as soon as I've tried it.

I'm presuming here that you want low lying smoke as popularised by horror films. 

Unfortunately there's no easy way.  Smoke, like water, is hard to scale down so you may find you need to shoot it on a larger set to get it to look right.  One way to do that is to block out the basic shapes from the set that you need the smoke to move around eg. if it needs to flow over a log or round a tree, set these up on a larger scale set in roughly the places (from the camer's perspective) that you have them on the stop motion set.  They don't want any detail, they need to be painted black or covered with black cloth. Pour your smoke over them and shoot it in the highest definition video you can.

After that, using a luminance key function - available in a lot of editing packages including Premiere, After Effects, Avid and FCP and even many consumer programmes: Pinnacle, Ulead 10+ etc , you can remove the black, scale the video to fit and be left with smoke that appears to curl and move around your miniature scenery.

There are various guidelines about shutter speeds and lens ratios when working on two different scales but they're so specific to each particular task that it's as well to just try things out until you find the right balance.

Shoot the animation first!  That way you know what the smoke needs to do and if you really want to go to town, dress in black and move through the smoke where your character has done so and with enough precision you'll get nice swirls and licks around their legs.  That would be pretty exciting!