A quick online search says that the role of cup-bearer was a high office. Nobles and kings have been cup-bearers to emperors, and the position entailed a great deal of risk on the cup-bearer’s part (they sometimes tasted the wine) and esteem from the person they were bearing cups for. If this is accurate, is it historically inaccurate for nobles in Westeros to take children and have them serve as cup-bearer? Or was this a position given to high-ranked up-and-comers?

He’s sort of mixing two different offices – cupbearer and page. As anyone who’s familiar with Crusader Kings II knows, cupbearer is an important office that you can give to men or women, which is handy if you’re trying to improve your wife’s opinion of you so you can start making some heirs. 

Pages, however, were noble male children in service to a knight or lord. And among their many duties might be to bring their knight or lord food or drink as request. 

So GRRM simply combined the two, because he wanted a way for Arya to overhear Roose Bolton.