When riding on ice you should do as Loudin Wainwright III said in
The Acid Song: “don’t laugh and don’t fart and don’t sneeze”. Don’t try to turn corners. Don’t try to brake. Don’t try to shift your weight. You should act like you are on eggshells. If you have to turn, do very, very, very wide turns without leaning the bike.
If you have to brake, do so gingerly and sparingly. Use the rear more then the front. If you use the front, just realize that it takes very little brake pressure to lock the front. You won’t go over the bars but the front wheel will immediately wash out and put you on the ground. The rear is going to slide as well but it won’t put you on the ground as quickly as the front well.
Shifting your weight is more involved with pedaling than anything else. If possible, coast over the ice if it is just a short patch. Put your feet parallel to the ground and glide over the ice. Don’t coast like most people do with one foot down and one up. You are more stable if your feet as parallel to the ground. If you have to pedal, do so as smoothly as you can. Try not to rock the bike in any way.
If you do fall, keep your hands (and arms and legs) inside the vehicle at all times. Our monkey minds work really well at walking speed and we can probably “catch” ourselves when we fall at walking speed. At running speed, trying to catch yourself in a fall is probably going to result in skeletal injury. At about 4 times walking speed, putting anything out to “catch” yourself is just going to result in gravity trying to break it off for you. Ride the bike down. Keep attached to it. Hang onto the bars and let your larger muscle mass...your hip and butt...take the impact. There’s more meat there and meat does better at impacts then bone does.
Studs will make a huge difference but like many others, I don’t run them the whole winter. Roads here aren’t icy for more than a few days after a snowstorm and studs are horrible to ride on pavement. Being able to ride over short icy patches is a skill that is good to develop.