Amazon and eBay have 'winter studded bicycle tires' for a mountain/frozen lake bike. Plus, these large volume tires could maybe keep the bike afloat? Plus, you can always walk a bicycle, and carry stuff in bike saddlebags.
https://youtube.com/watch?v=Y6s1SPar2ao ... Bike on Ice .....7:57/Feb 2016 .... cycling a tandem bicycle on giant Lake Baikal in Russia ... while it does not say, those tires must be winter studded tires for that smooth ice. Looking closely, you can see a straight line of tire travel etched into the smooth ice, which would indicate studded tires here.
What with all the icy cross country ski trails, Waterville Valley has 4" fat tire bikes it rents out for pedaling the cross country ski trails.
Someone needs to invent a tire where you push a button, and the spikes extend out for extra traction, just like a cat's claw, to adjust for changing conditions.