I got my first flat on my Continental CityContacts a minute after I thought to myself, "wow 1000km and not one flat, these tires do deserve a better reputation". I have since learned not to think too positive
In my experience, ice that is melting and covered in water is much more slippery than when it's freezing outside. Running studded tires is noisy, but I can go pretty fast without minding the ice at all with a pair of Marathon Winters, especially during the dark hours when I otherwise would have to be very careful and watch out for ice patches.