The main reason most people will go to Chyllfroest is for the local mount, the Ursagrodon. In order to tame the Ursagrodon you need a Melting Horn; to get it, hunt Chakoyas for a Fireproof Horn and use the Tinder Box you find on top of the Chyllfroest Mountain on it. The Ursagrodon appears not as a monster but as a frozen skeleton in a wall of ice. Several Ursagrodons exist on several floors, but the easiest spawns are on the east side of the first floor underground. Use the Melting Horn three times on the Frozen Ursagrodon to thaw and tame it. The chances to succeed seem to be very low, and if you fail your Melting Horn will break. Therefore, many players choose to bring alternative characters to obtain the quest-only Tinder Box. The Tinder Box can be reobtained after waiting 20 hours.
As for hunting opportunities, there are four main areas you can hunt:
Not really worth hunting here, because well, Chakoyas just aren't. But if you want to tame the Ursagrodon you may want to hunt them for Fireproof Horns, which you can then use on the Tinder you can find on top of the mountain to obtain the Melting Horn needed in order to tame one.
At the south-west part of the cave there is a wrecked ship. Just by the ship is a Pirate Skeleton and an unreachable Pirate Ghost. This may have an important backstory, but nothing is known about it.
Besides the Chakoya dungeon there is also the Chyllfroest Mountain. This mountain contains various hunting grounds for a few level ranges.
In particular, floor -4 and -5 contain a lot of mid-level creatures; floor -2 contains a very high level cave; floor +1 to -1 contains a ton of Frost Dragons.
The Ursagrodon is also in this mountain. On the 1st floor underground on the east side, the ursagrodon is frozen in the ice and must be thawed out (the ursagrodon does not actually exist as a creature).
Keep in mind that you can walk around the perimeter south-east of the mountain. Thus, you do not need to pass the frost dragons to reach the ursagrodon.