Yes - you’ve combined niche construction with neutral theory before, and it makes sense. Still, we’ve got a selection scenario - there’s no guarantee that the change in cold tolerance would not disadvantage the animals with the mutation, which would be moving away from the environment they’re generally adapted for.
Niche construction is also one of those theories, like sexual selextion, that assumes prerequisites, like the nous to construct the niche when your genes start messing you about. Your example of feeling cold is nice and simple, but it also has to explain anteaters and moles.
Blimey, straight from Romans 5 to niche construction. This never happens in seminaries, I bet.