In Game of Thrones S08E03 we see Ghost charging with the Dothraki to fight the dead army, but could he kill them?
If no, how could he be useful in that charge?
To drop this to an answer, from comments...
I think we can assume Ghost can kill wights, though not White Walkers.
White Walkers can be killed only by dragon glass or Valyrian steel.
Wights, on the other hand, we have seen killed many times by more 'simple' mechanical means - blow them up, decapitate them, or otherwise heavily dismember. 
We have on the odd occasion seen that a surviving hand can move on its own but I think that has only happened when it was 'just' dismemberment, ie the rest of the wight was still 'alive'.
I checked the wight at King's Landing (S07E07) - that was in 2 halves & still both halves moving, then the hand was removed & that kept moving. Jon killed it with dragon glass [whilst telling everyone it was that or fire, even though we've already seen otherwise at Hardhome (S05E08).]
 Arrow in the head; trod on or pulled in half by a giant; couple of sword-thrusts through the body; axe in the back - all these from Hardhome.
Wights can be killed by fire, dragonglass or valyrian steel. Ghost has none of those, so is useless.
Note that the same went for the Dothraki until their Arakhs were set on fire.