The cuyote do go out on the ice. I was scanning the lake with a PTZ survellience camera a few years back and found a cuyote a few miles out on the ice. He was traveling between the packs of birds feeding on the dead fish protruding from the ice.
Burke Airport in downtown Cleveland along the harbor has cuyote as well. They keep their cuyote population at one. No more. They like the one because they eat the nesting bird eggs. The airport traffic does not mix well with birds. Birds took out a Thunderbird during an airshow a few decades back. The pilot did not survive.
The most majestic wild beast I have seen in a long time was a cuyote/black lab mix. It was chasing/tracking a fawn. It was about an 80# cuyote. An Alpha male.