I downloaded the HD texture pack DLC from steam recently but as I played I noticed that an increasing number of items were losing their textures. I would load the game and most everything would look fine, then I would go outside and come back and character's clothing or items would be textureless, etc.

I decided to delete the texture pack through the data files menu, but now I have no way of reinstalling them.
Steam doesn't seem to recognise that the pack is gone.

Have you tried reinstalling the whole game?

that seems like overkill, considering the original textures work fine