Here’s an interesting riff on the basic tire chain by Dutch designer Cesar Van Rongen. A set of flexible plastic strips are attached by two pieces of wire (think of a tire bead) that is wrapped over the tire and tightened into place. Studs in these strips provide traction. Easy on / easy off, according to Van Rongen. Video below.
Studded bike tires are the usual solution to the problem of biking on ice. Modern studded bike tires from reputable vendors are very well engineered, with thought put into stud material and placement. Bicycle tire chains are also available.