so, doesn't your kink confirm that "gheim" IS the base for winter?

No, goofy's link shows that the PIE root glossed as winter is the origin of Latin hiems 'winter], hibernus] 'pertaining to winter', (it's also the source of Sanskrit hima 'cold, frost; snow' whence Himalayas the mountain range). Some derive English winter (and the other Germanic words like German Winter) from PIE *kweid- 'white, light'.

Ceci n'est pas un seing.