Do Ashkenazi Jews represent all Jews? No, they don't. There is a reason the term Ashkenazi exists separate of the term Jew. Because you can't use it to represent the totality of Jewry, you can't use them to "prove" such a claim. True, most Jews tend to have some Ashkenazi ancestry; however, the amount of non-Ashkenazi Jews is large enough to make such claims based on just one group worthless as a generalization.
However, are Ashkenazi Jews white? According to white supremacist types...no, no they aren't. While most people wouldn't consider them the highest authority on such matters, it is worth noting that the concept of race is a bit more complicated than most people take it to be nowadays. Until the 1960s, most people didn't take Ashkenazim to be white even if they weren't anti-Semitic, and even Jews saw themselves as something "other" and at best could "pass" as white. Ignoring that racial terminology, it's worth noting that Ashkenazi genealogy is distinct from surrounding Europeans. It's closer to other Middle Eastern peoples, such as the Kurds....or, obviously, Sephardi and Mizrahi Jewish groups. The classification of these groups as "white" isn't standard and besides, most people consider them "non-white" nowadays.
In the end, the proof that "Jews are white" is utterly destroyed when you consider groups like the Ethiopian Jews or the Chinese Jews, or simply converts who are NOT white by any stretch of the imagination. Even if Ashkenazim were the whitest of the white, there are counterexamples which prove your generalization would still be wrong.