The spell Cone of Cold states:
A creature killed by this spell becomes a frozen statue until it thaws.
By "statue", does it mean the body is frozen solid, or that it is frozen inside a block of ice?
The quote you gave states that "the creature ... becomes a frozen statue", which I read to mean the creature themselves is frozen, not that they are encased in ice.
Contrast this to the warlock Eldritch Invocation "Tomb of Levistus" (XGtE, p. 57), which states:
... you can entomb yourself in ice ...
This implies that cone of cold could have used similar language, but didn't, so probably ought to be taken literally, meaning that they are turned into an ice statue.
I can't think of any mechanical effect that this distinction would make a difference and the language in the description is pretty broad. Talk to your DM(or your player if you are the DM) and narrate with what works in your shared world.
The spell is clear that the corpse is not a corpse, but a frozen statue until it thaws. Any mechanic that deals with a corpse must wait until it is no longer a frozen statue (when it thaws.)