An interesting subject.... and several of the posts seem to be headed in the right direction. But ice is a very fickle material in its mechanical and physical properties. So, be very careful; just a few practical additions to the thread....
We always talked in terms of about 4" of ice for safe walking or skating. But I’ve walked on much thinner ice with some trepidation, in not too deep a water situation. You can feel and see it flexing just before you fill your boots with water. This is very dangerous where there is any moving water since it can keep the ice from forming despite cold weather, it melts it from below. Rivers or streams are an example of this all season long. You must know the lake, because a lake bottom spring entering the lake, 20' below the ice will stir the water enough to keep the ice very thin. With no guarantees, we thought: about 5" of ice for snowmobiles and ATVs; about 8" for compact cars; about 12" for light trucks, spacing of these heavier loads are at your own risk.
Snow acts as an insulator, so if you get ice and then snow too quickly, the ice will not develop thickness very quickly. The weight of the snow may actually depress the thin ice, slowly, with water coming up through cracks or weak ice and forming an inferior (not strong) ice/snow mix. Some compressive strength once it freezes, but no tensile strength. For ice roads, as quickly as you can get a light plow on the ice, you want to plow the ice road very wide, so the ice will continue to form a nice wide, and thick, roadway.
There is a buoyant force (the elastic found.), force/stress transfer through the ice and away from the point load area as Teguci suggests, and there is a confinement/pressure mechanism going on as the ice deflects under load as Sail3 suggests. This shows up in the form of water geysers or artesian like water, flowing up through cracks in the ice in the vicinity of a heavy load like a car. This must be in the form of a ice stress/deflection and buoyancy/pressure wave moving along under the moving load. And, you can see the two sheets of ice displace w.r.t. each other as the wheel goes over a fresh crack. I have had ice crack right under my feet, suffice-it-to-say I was glad I relieved myself before I left the house. I have had ice cracking behind me, with water welling up through the cracks, using a snowmobile. If you keep moving, you can stay ahead of it and get off the ice. I’m sure that if I had stopped I would have been fishing the snowmobile out of the lake. This happened during an age where I thought I was more invincible than I know I am now.
