Do Dogs Understand Phase Transition?

Yesterday, in an attempt to get some vitamin D and dispel the cold and dark winter blues, my wife and I tried to take a hike at the Rutgers Ecological Preserve-- but the trail was coated in a layer of ice covered by a dusting of snow: it was way too slippery to traverse hills and navigate cliffs-- and so we changed plans and drove over to the Raritan Canal Path, which runs between the river and tow road; we figured even if it was icy, at least the trail is flat-- but there is a small hill at the start of the trail, which leads down to where the first lock used to be-- now it's a stone dam-- and the hill was a sheet of ice, so I let Lola off her leash so she wouldn't pull me over and further destroy my bad knee and she hurtled down the hill and onto the thin ice covering the canal and promptly fell through the ice-- but luckily she managed to get her front paws on the stone of the dam and I quickly skated and slid my way down the hill and pulled her out of the freezing water before she fell all the way in . . . though it all happened very quickly, it was a hairy couple of moments where we thought she might plunge under the ice, never to be seen again-- but she was lucky and hopefully learned her lesson about thin ice (though I did keep her on the leash for the rest of the walk).