Sorry to hear you got hurt, glad it wasn’t badly
Bikes and ice just plain don’t mix, add in fog and you are really stacking the odds!
You run the risk of black ice at 4c and wet or 3c and dry. It’s not just you but the other road users who may lose control and hurt you.
Those may seem like pretty high temps but everytime I’ve broken that rule I’ve found ice or it’s found me, in one case at 25mph in a dip