In winter, is it possible for two distinct bodies of water, which are a few kilometers apart (so they are exposed to roughly same temperature), to have different thickness of ice? Does the area of the surface, total volume, or depth have any significant effect on the ice thickness?
The answer is yes. As an (extreme) example, consider a large lake, and a puddle of water on a sidewalk next to the lake. Once the air temperature drops below freezing, the big lake still has to lose a lot of energy to cool to freezing, and that takes time. Meanwhile, the puddle can freeze quite rapidly, since the surface area to volume ratio is quite large.