Some of us don't have a choice since we have two choices when it's icy; walk or ride. About a hundred pages ago i posted about the handful of times i'd come off my bike in icy conditions. My solution wasn't studded tyres, nor was it buying a helmet... it was riding more cautiously when the conditions dictate. Please, don't take this as 'advice'... it's just how i managed to think my way through a problem i faced.
I ride on the trikes on days I would not contemplate on two wheels, as with you, my personal solution