I sent a request to the council after seeing the map to see if they could add the new(ish) Chancelot Path to their cycle path gritting list.
Response today:
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ADDITION OF CHANCELOT PATH TO CYCLEWAY GRITTING ROUTES
I refer to your communication of 22 October regarding the above.
Having now discussed the matter with Services for Communites Cycling Development Team, I have agreed with them that Chancelot Path will be given a higher priority status for winter maintenance in keeping with the other major parts of the off-road Cycle Network in the immediate vicinity. As a result the stretch of path you identified in your correspondence will now be added to Road Services priority cycleway gritting routes.
This addition will be reflected in our online map of winter gritting routes at the next update.
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Small yay!
Of course "in keeping with other major cycle paths in the vicinity" in reality means "very occasionally", but hey ho, better some than none :)