This was been checked thoroughly and indeed we found something to tweak and fix.
The snow movement penalties itself were working flawlessly when it comes to the speed an animal can move in the deep snow.
However, there were few faulty calculations in fatigue rate which animals suffer when moving the snow. This could result either in animals tiring too easily, or too little. The issue appears on border areas of certain snow depths, so that's why you have rightly noticed the dogs not tiring in the deepest snow.
In most cases the snow penalty system is working as it should, but some oddities may be witnessed - as you did.
It should be noted that animals which are adapted to moving in the snow can and will still get tired. Even if a hare would run on solid surface in the summertime, it will eventually tire out if it can't rest every now and then. This can naturally happen on snowy surface as well, even though hares are adapted to moving in the snow. The same goes for the lynx too. So we don't actually know what tired that lynx out. It could have been this issue, or the lynx might have been running after the game just a little earlier. For the many reasons this glitch isn't easy to spot, and wasn't easy to discover from the code either.
But it's great that you paid attention to this. We've found the issue and the snow related fatigue accumulation issues will be fixed in the next patch.
Fixed - persists in 3.70.