We seem to have solved half the mystery — alas, the easier half — of what to call my favorite cookie. About a hundred of you have written in, including a half-dozen folks from Australia where the little colored balls (excuse me, coloured) are known as "Hundreds & Thousands." Others suggested they were called "sprinkles," "dragees" or even "round jimmies."
But the consensus seems to be — and many of you sent links to pages that sell them under this name — "rainbow sugar nonpareils." Some sources hyphenate the last word and some spell it, "nonpariel."
Okay, that's what the decorations are called. Now, what are the cookies called?
I have about a dozen answers, no one of which was given by very many people. So I'm leaning towards the theory that no one is widely accepted. I'll wait a few days to see if anyone convinces me otherwise and then I'll post some of what I've learned.