Around here (New England) any food taken after 10 p.m. is usually called "a midnight snack" not supper.
Is that a US-only saying? Or do you use it across the pond and up North? (Hi Bean)
If I "have tea" in late afternoon it's usually just a cup of tea perhaps with a cracker/cookie/toast if really hungry (no lunch!) This is what was called "A cup in your hand" in Ireland - rather than High Tea!