To get the item, a lvl 15+ can do it, defeating chakotas is pretty easy in almost any level if you are careful and get enough supplies. All the west side of the pensinsule is full of them.
To tame the mount you will have to face Wyvern and Frost giant. So I would say that you would need over lvl 30+, probably less depending of your skills.
To get into the respawn for sure it is better to go by the surface in order not to face frost dragons.
This is the best option for you:
You need to go downstairs in the marked stairs, and there you will face the wyverns and frost giants.
The marked spots, are some of the ones where you can use the melting horn to tame the mount.
Hope I helped you :)