Incidentally, @PeterShor, we know this wasn’t PG since fronting of /a/ to /æ/ did not happen with nasal vowels or before nasals in Anglo-Frisian, though it did (later on) in German. In PG, the word was still
*gans-, with a nasal present, and this developed regularly into ON [ɡɑ̃ːs] (written
gás) and West Germanic [ɡɑ̃s]/[ɡɔ̃ːs] with compensatory lengthening, but Proto-German [ɡans]. Only after the nasality of the vowel was lost in WG (yielding [ɡɔːs], later raised to [ɡoːs]) did i-umlaut take place. If it had been earlier, the plural would have been
*goose as well. —
Janus Bahs Jacquet Jan 17 '15 at 11:06