You can see the difference how it looks in November and January.
It was cold in November but no snow where as in January it was snow while hiking Kala Pathar and Everest base camp.
Yes it is October & November is best time to trek Everest base camp but it's not that bad in January also.
You just need to use crampons/gaiters.
Pictures are by Lukla Porter.
Thanks
KS
