Based on recent adventures, most sections are passable at the moment. That said, as things stand the main tricky bits are…
Garrigill-Nenthead (off road is a ski route at the moment, but probably passable with care on a bike, the road version is passable but some potential for suicidal conditions when it refreezes).
Nenthead-Allenheads (this is mostly clear road, but surrounded by big drifts, some icy bits)
Allenheads-Rookhope (currently the road is clear at least one car width, but drifts are over 2m deep on the climb out- if you're into jumping road gaps, it's a good one).
Out of Rookhope (off road I'm unsure, was skiing round that way earlier in the week, the aspect favours it being largely clear lower down with only short sections badly drifted towards the top. The old railway will probably be snowy but not more than 1m deep at most. On road fine).
Generally, the snow is hard packed with a few (5-25) cm of softer fresh stuff on top, so not the worst to ride on, but it will be a pain on the off-road sections if there was a sudden thaw. Snow line is around 400m, depending on aspect, varying from valley to valley and with some significant drifts.
The route would be fine just now I reckon, depending on how willing you are to deal with snowier sections. You can always divert pretty easily onto the road, though some of the smaller ones round the official route still have 'closed' signs up (mostly they are to stop people getting stuck, but seeing as locals have to use them to get to their homes they are being used- just some 'interesting' bits- so should be no problem on a bike). The main problem will be if there is snow with wind before the weekend- many sections of road will not take much to block them so won't make viable alternatives.
I'd say go for it, but keep an eye on the weather forecasts and use common sense if things get/look bad.
[edit] when I say 'passable', that means 'doable'. I wouldn't always recommend it to others though.