While the concept of using chains on a bicycle is an interesting one I doubt they can be made to work particularly well, unless one grinds the links to have lots of sharp corners. The way I understand motor vehicle chains to work is, that the harder than ice steel chain breaks the ice beneath via sheer mass of the vehicle. The chains have tiny surface area against the road compared to the weight of the vehicle. Mass is one of the reasons why studded tires for larger vehicles like semis or busses are a rarity. They don't necessarily need them because the pressure against the road exerted by the tires is so huge, which cracks ice and gains traction for the tires.

I don't think a bicycle has enough mass for chains to break the ice surface enough to aid with traction.

Anyways studs are a simple and easy way to deal with ice on the roads. But they're not bulletproof either. You can't corner normally on ice even with the studdiest tires on the market. I have Schwalbe Al Mighties and have washed out a few times with them.
Better to focus on riding straight and level. When an icy corner comes along, slow down properly and maybe even put a foot down for support.

Tire pressure is something I've been pondering. More tire pressure means less studs contacting the road. I'm not sure however, whether more pressure increases the "pressure" a stud pushes against the road, since the studs are elevated. My gut feel and experience tells me lower pressure is better on ice simply due to having more tire surface area and studs available for traction.