I walked from Wasdale to Wasdale in summertime a few years ago - camping at Kikstone Pass and Angle Tarn. The second day was quite hard, I seem to remember. It wasn;t the TGO route, though, ours was very direct.
In summer, the route is pretty straightforward, but in winter, you'd like experience either mild, wet and very windy weather/ potentially severe gales with cloud bases around 300 metres - possibly with snow/blizzard conditions on the high tops with temps at, say 6 to 10 degrees C ...OR .... very settled, cold, frosty, icy weather, possibly with temperature inversions, with very light winds and temps around 1 0r 2 degrees daytime and down to minus 8 or 10 (potentially minus 15 ish) at night.
UK weather tends to toggle between the two in winter.
You'd need good waterproof and warm kit and winter equipment, specially ice axes.
Daylight in early January would be from 8:15 am to about 3:45 pm, so you'd need good lighting recources.