I'll give my view: I can mentally count, but to the extent there's anything visual about it, it's more as if I'm reconstructing from a spatial memory rather than seeing anything. I can "force" a very vague outline, which is more constructed than remembered (I know where the bed is, so I can "force" myself to sort-of see an outline of a bed, but it will be a generic bed, not my bed until/unless I focus on explicitly go through the details of how my bed looks).

Same for faces. I'm badly out of practice when it comes to drawing, but I can draw objects and faces with a lot more detail than I can visualise them.

EDIT: Reading post, to him it certainly goes far further than for me. I absolutely do imagine things, just not visually. I can describe things verbally without having to remind myself of the words the way he describes, but I don't see them. Consider how a blind person might remember what you look like and be able to recall and describe it based on memories of having touched your face. A bit like that maybe, except without the touching your face part.

I certainly do dream with some degree of visualisation, though I can't remember any of that visually once I'm properly awake.