Currently on my ss mtb I have a studded 2.1" tire in the front and a knobby 2.3 in back. In the past I've used two studded tires and have found that I prefer to remain seated when climbing very steep hills because the rear tire will occasionally break free. That said, you can usually "pick your line" up through icy hills and find less slippery spots where you can boost your power by standing for a few seconds.
Width of studded tires is up to you. Narrower tires with fewer studs make for a rougher ride over rutted ice and rough terrain. Fatter studded tires are slower and have more rolling resistance but add a lot of control in very very icy conditions and will cushion your ride through rough terrain.
Here in MSP we had a sudden deep freeze (temps at -10 F today) that froze a lot of the snow and water on the roads creating some major ice ruts. When I'm riding my bike with 2 35mm studded tires it can be very rough and hard to control through the ruts. On my ss mtb with two fat tires, only one of which is studded, the riding is easier because I have more stability and my traction patch is much larger.
In my opinion, if you are facing a lot of icy and rough terrain, I would go for the 40+mm studded tires. If it's more of just smooth ice glaze, the 35s should be just fine.
Good luck with your riding!