I've answered the poll, of course, but here's a somewhat more extensive description.
I'd say my characters tend to encounter recoverable carcasses of drowned elks and reindeer around once per game year, possibly up to twice per year. It helped my last character that two traps were close to the water, so those areas were visited essentially daily. My characters tend to settle beside rapids for the easy access to water in addition to the defensive value of having one side safe from attacks, which means at least some travel along the (ice covered) water happens.
As an example, during the character's last autumn an elk was seen wandering around the area of the traps, and one day, on a hunch, the character decided to take a closer look after having seen the elk in the distance on the river tile, and sure enough, the elk was found drowned (although that's the only time I've actively looked for a specific animal, but I've walked along the shore a number of times to check for signs of elk/reindeer straying out onto the thin ice, and have found such victims several times, as well as ones that are still alive and struggling, with my character just sitting back and watching for the struggle to end so recovery can be commenced).
This comes in addition to actively scaring animals out onto thin ice as a form of active hunting, which I think works about as it ought to (maybe a bit on the easy side, as the animals might be a bit more reluctant to move out onto thin ice rather than moving along the shore).