On a mini theres not much you can do
- Ensure no water leaks
- Check if carpets are damp etc.
- Use rubber mats to prevent water from feet soaking into carpets
- Make sure the windscreen is clean and dont wipe it, this only makes it worse next time.
- Heater on and turned to windscreen setting. Open drivers window 1/2 inch.
I used to have a dehumifider bag thing on the parcel shelf and one by the dashboard. You can get them on ebay for under a tenner (for a pair) and they can be dried and reused. I got a type which were in a bag which laid flat and was heavy enough not to move (unlike the cheap plastic type you get in the supermarkets).
Theres also heated windscreens available to buy. Also anti fog type stuff, but never tried this myself.