Does Voldemort know? Did Snape tell him?

[Kenneth Clark]

No: HPFGUIDX 160723

When Dumbledore returned from finding and destroying the horcrux in the
cottage with his hand cursed and blackened he didn't keep his injury a
secret.  Harry noticed it staightaway and it was immediately spotted by
others on the first day of school.  Word must have got back to
Voldemort from Draco (and others) of this injury.  Would Voldemort not
have recognised the injury as one which would have come from his curse
defending his Horcrux or similar?

Dumbledore says that the injury would have had a more serious effect
had it not been for the assistance Snape gave him.  Did he tell Snape
what had injured him?  Would he have had to in order for Snape to work
out a suitable remedy?  If Snape is with Voldemort then he too would
almost certainly have told Voldemort what had damaged Dumbledore.
Would such information not had alerted Voldemort to the possibility (at
least) that one Horcrux had been located?

Dumbledore says that he trusts Snape completely.  Perhaps he can say
that because he has entrusted Snape with the secret of the existence of
the Horcruxes?  Even if he has only told Snape that he was doing
something that caused the curse to hit him Snape would know that this
information would be wanted by Voldemort since whatever Dumbledore was
doing had to be something to do with fighting Voldemort.  Voldemort
would have to be pretty stupid not to make the link between what Snape
would have told him and his Horcrux.

We are therefore left with the two possibilities. Either Snape is on
Voldemort's side and has told him all which would mean that there is a
better than even chance that Voldemort knows that Dumbledore (and
Harry) know about the Horcruxes.  Or he is not and has told Voldemort
nothing (or something anodyne) about the cursed hand which still leaves
the possibility of Voldemort making the link himself based on the open
knowledge of the withered hand.

Kenneth Clark