For ice and hard surfaces ridges don't do much, it is the material that matters. Go for rubber soles eg, tennis/squash shoes.
You only need ridges for snow or mud, but there studs are better than ridges (look for orienteering shoes), but they don't work so well on ice and hard surfaces.
For an all rounder you are best looking at walkers trainers which have a mix of studs and thick ridges to provide a decent compromise of performance on both hard and soft surfaces.
I wear DC skateboard shoes anyway but find they offer great grip in snow and ice. I once managed to walk on ice pulling along a friend who grabbing onto me but not moving their feet and didn't lose grip
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You only need ridges for snow or mud, but there studs are better than ridges (look for orienteering shoes), but they don't work so well on ice and hard surfaces.
For an all rounder you are best looking at walkers trainers which have a mix of studs and thick ridges to provide a decent compromise of performance on both hard and soft surfaces.
...such as yaktrax and the like: https://www.google.co.uk/search?q=yaktrax&source=lnms&tbm=isch&sa=X&ei=Xf9iUoaLE4uqhQe-mYCAAg&ved=0CAcQ_AUoAQ&biw=1024&bih=578&dpr=1
sorted
http://www.amazon.co.uk/gp/product/B001CZEYGI/ref=oh_details_o08_s00_i00?ie=UTF8&psc=1