I've used both Top Contact Winter II and Marathon Winter studded. Both are quite a lot better than standard tyres, and both still require the use of care to avoid falling off.
It's much as you might expect - Top Contact are quite a bit nicer to ride, but aren't as good when you are actually on ice, though I didn't spin out until the slope got to about 8%. Translate that to a cornering lean angle to get an idea of how far you could push a corner. This was on cold dry ice (-5° or so), not warm wet ice at around zero, which is a fair bit slippier.
Marathon Winter are by comparison fairly heavy and slow, not to mention noisy. On ice you should reduce pressure to get more grip. If you don't there may only be a couple of studs in contact with the ice, or even none if the ice surface is uneven and the stud is over a hollow. DAHIKT.
Winter tyres aren't absolutely necessary. It is possible to get round reasonably well on normal tyres (gatorskins or Conti 4 seasons), but you do have to take care. Taking care means paying very close attention to the road surface well ahead, and being prepared to slow right down to walking pace (gradually) if you think you may be on ice or about to run onto it.