Trekking to Goechala in the winter months is extremely difficult (close to impossible). The slopes will be steep with ice. Trekkers will require prior experience and proper equipment for this trek.
The best time to trek is from April last week to June end. In January there is too much ice and it is very risky. Slopes are steep with ice, you need guidance and equipment. If you are set on a winter trek, It is best you do this in October and November. Mid September to October end is the time for spectacular views of the Kanchenjunga. Trails strewn with rhododendrons gives the trek a poetic charm.
I wouldnt suggest that trek in january first of all due to its harsh climate and secondly even doctors availability during emergency is also not available
This is already one of THE most challenging treks counted by many as even wilder than Chadar or Roopkund. I would recommend you not to undertake this in JANUARY.