I don't know -- I'm going to go with no. The most famous reference to ice in the Hippocratic corpus is in De vetere medicine (On Ancient Medicine), about using ice to stop gynecologic hemorrhage.

I have no idea where that quote comes from; I did a quick Dr. Google search and found only unsourced references on ice cream sites. Furthermore, the translation is super weird. I assume that "lifejuices" is a bizarre translation for the humors which I've never seen before. And honestly, that's why I don't think it's a real. Now, there's a lot of disagreement in humoral theory about what foods favor which humors, but there seems to be a pretty good agreement that application of ice leads to an over-production of phlegm. In Aphorisms (24), Hippocrates writes: "Cold things such as snow and ice are inimical to the coughs of discharges, of blood, and of catarrhs (in this context, phlegm)".

So I'm open to being wrong here -- but since the quote appears to invoke humoral theory, and humoral theory was used to justify no consumption of iced beverages (though again, with considerable heterogeneity), I think it's probably not a real quote.