Have you tried various companions from the modding community? The most advanced one so far is Viljia. There is also Valtiero, Stalker wolf, Neeshka, Ruin tail, etc
I think what you will find from one to another is flaws and qualities that will make a companion complete or not. Maybe you already know all Im saying but I'll say it anyway >.<
A companion is appealing through his/her dialogue, that is its essence.
What you have to consider is how the companions interact with the environment - you, the other npcs, the world, the quest, the lore, etc
Its through its interaction that a companion truly comes alive no matter its profession or how well he fights or even is alignment!
Personally, I like your idea of a snow bred Khajiit and the fact that he can sing and how he could be shy about it is funneh!
Quest is always a plus, or several small quest, its a perk you give to your mod or it can revolve entirely around it (as in Ruin-Tail).
No matter how evil, good, intelligent, stupid, cute, horrifying your companion will be, it always comes down to its essence, past the mesh, texture and animation =D