Why did he take his clothes when he slept inside the horse?

I'm not an expert about these things at all but my guess is that since his clothes were already cold his body would absorb heat faster and better if he took them off, it would prevent the heat from coming or make it coming slower.

He had to be naked for the reborn metaphor

His clothes would be converted in blood to defrost and refreeze. Better to have them off.

Clothes isolate your extremities body heat, because clothes and the layer of air are insulators. This means sleeping in a sleeping bag naked will keep you warmer when naked than when clothed. Think of it like mittens vs. gloves. So why wear pants and a coat instead of zipping yourself up in a giant potato sack when exploring the outdoors? Because rolling your way to Grandma's is not practical.

I remember other frontier Indian stories where it's a bad idea for avoiding getting tracked by either animals or humans to have blood frozen onto your critical equipment - a knife, clothes etc... No idea if that's true but it was definitely in other fiction about the same era.

I am no expert on this either, but injured or wounded people, especially hunters in my region (used to) lay inside an animal like this, or cover injured parts in rabbit or sheep carcass (with no organs) because there is something about their fat that makes injuries heal faster. It's an ancient 'medicine' apparently. Having clothes on would make little sense.

He could generate more body heat without his damp clothes against his skin

You know what? From what I gathered from this thread, there are a combination of reasons for him sleeping in the horse naked.

Basically, it's to keep warm, to not get blood on his clothes because its scent could attract the Arikara and animals to him, to use the horse's fat, blood, and other bodily fluids to further dress his wounds, AND it's a metaphor for rebirth.

I'd like to add one more. Since the horse belonged to Hikuc, the man who saved, helped, and befriended him, it also could be a symbolic way of his friend once again helping and protecting him. Even from beyond the grave. Especially if Hugh at one point laid his hand on the horse's body after the fact seemingly out of gratitude and out of respect for his friend.