I agree that it depends on the adult and the pony.
Ziggy is technically a pony because he is under 14.2 (I have never measured him TBH but I reckon 14.1 tops) and he has a pony brain. However he can easily carry 12 stone, and he isn't what I would class as a child's ride either!
His friend Billy (the other grey in the recent pictures) is a 13.3 or thereabouts New Forest, but he is much finer in build and couldn't do more than about 9.5 stone comfortably. As Notpoodle says, he has been pushed from pillar to post - he is 18 and has had at least 6 owners, all of whom have used him hard for Pony Club activities because he is a sweet, kind, forgiving, goodnatured, able pony.
There are not many adults as small and light as Joosie, VIcki100 and Cherifen, able comfortably to ride a Welsh Sec A or B.