The Tur discusses different opinions about cutting nails. Then he ends the siman by saying all refu'ah is muttar on chol hamoed.
What's that got to do with anything? What is the connection between nail cutting and refuah? Why is that one-line ruling here and not elsewhere?

[By the way, in terms of practical halachah, I'm not sure that literally all refuah is permitted according to all authorities today].

Perhaps personal grooming is part of refua. (or maybe having long nails is sick?)

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Could be, but if I had to guess, I'd say that ruling about refuah should have been in the previous siman about haircutting given the connection between barbers and surgeons in the middle ages.
http://www.faqs.org/health/topics/21/Barber-surgeons.html

doesn't it hve more to do with prep for the chag; if yu cut on erev you can cut on chol. assming you're not a lady preparing for tevilah.

A baby who will scratch themselves can have their nails cut on Chol Hamoed, right? Isn't that "for refuah"?

Without looking inside I'd guess that although by modern medical parameters having long nails is not harmful as long as proper hygiene is followed, having long nails was considered in the Tur's day to be harmful to the person and thus cutting them was refuah.