I don't recall saying he spoke of "half-dwarves" as, say, a role-playing gamer would speak of them. The reference is to the army that took Cair Andros and crossed Anduin there to block the road to Rohan:

  So now at least the City was besieged, enclosed in a ring of
  foes.  The Rammas was broken, and all the Pelennor abandoned
  to the Enemy.  The last word to come from outside the walls
  was brought by men flying down the northward road ere the Gate
  was shut.  They were the remnant of the guard that was kept at
  that point where the way from Anorien and Rohan ran into the
  townlands.  Ingold led them, the same who had admitted Gandalf
  and Pippin less than five days before, while the sun still rose
  and there was hope in the morning.



  'There is no news of the Rohirrim', he said.  'Rohan will not
  come now.  Or if they come, it will not avail us.  The new host
  that we had tidings of has come first, from over the River by
  way of Andros, it is said.  They are strong: battalions of Orcs
  of the Eye, and countless companies of Men of a new sort that
  we have not met before.  Not tall, but broad and grim, bearded
  like dwarves, wielding great axes.  Out of some savage land in
  the wide East they come, we deem.  They hold the northward
  road;  and many have passed on into Anorien.  The Rohirrim
  cannot come.'

I don't recall Tolkien ever calling them Half-dwarves. I think the convention was developed by gamers and Tolkien fans have simply fallen into the happen of using that term.
------------------
Xenite.Org: Science Fiction and Fantasy