It's not just the tyres which are the problem. There is something wrong with the condenser so the windows always mist up - the wipers don't work properly and I am increasingly concerned about the brakes. A bit of a death trap all round in the wet really.
Cheaper than buying another car, fit all-season/mud & snow/winter tyres to your Scenic. Replacing a shit car on shit tyres with a good car on shit tyres will make very little difference.
If there's anything local, do a skidpan driving course.
These are both things that will benefit any car you drive.
If you're intent on changing your car and are concerned about grip and traction, I'd recommend something like a Subaru Legacy or AWD Impreza, quattro Audi or Volvo XC70 - something like that. Generally something with 4WD will give you that bit extra when you need it on the road.
We live in Scotland and somehow i often seem to be driving down the M8 in the pouring rain - or halfway up a mountain in the snow. Our 9 year old Scenic feels increasingly unsafe and I have to get a new (second hand car).