I've seen waist deep snow. I'm unsure if I've seen deeper than that, but can't rule out chest deep being possible.
The introduction of snow effects on animals and the introduction of crust makes major differences to animal endurance.
Snow now affects animals, so elk and reindeer tire very much faster in deep snow, and it seems to get worse the thicker the crust is. At the same time, a sufficient crust now makes it possible for the player character to ski without losing stamina.
I very recently gave up on trying to chase a glutton with my fast (7 km/h) character during "spring" (thigh deep snow still, I think) due to it recovering stamina completely even though I didn't lose its tracks more than very marginally, while elks and reindeer are fairly easy to hunt down in open terrain while skiing. They can shake off my player when getting into spruce terrain and have their tracks get into a mess of older tracks. I've found badgers to be very easy to tire out (both with and without snow), with the main problem being to track them (so open terrain is a great advantage).
Slower characters have a harder time and they require more luck when it comes to the prey movement (a straight line will allow the animals to recover stamina while moving), but with meandering and walking in circles it's still possible to hunt elks and reindeer down. However, even slow characters have been able to catch elks and reindeer, but the failure rate is higher (you can (ab)use the system to try to zoom in on the map close enough to an animal to hurt it with a javelin or arrow: with a bit of luck you're able to cripple them, which makes a rather significant difference to the difficulty of tiring them. Using arrows should be possible even at fairly large distances, although the hit rate will be fairly low. I haven't used broadheads, but I guess that would improve your chances of bleeding the prey out).
I'd say the Calle character definitely is on the poor side when it comes to tracking, although it matters less during the winter, but losing the track means losing time that the prey can use to recover stamina, and it means any spruce terrain is a gamble. 4 mph should be about 6 km/h, which I consider to be a fast character, so I'd be happy with that speed on a character of mine (I consider 4 km/h and less to be slow, and 5 km/h to be about average).