Thanks for the input guys!
I hadn't thought of pointillism - how silly of me.
However, I have to disagree on the main point: these cards are
not pointillist paintings or drawings, reproduced
as is.
No halftone
reproduction method is visible at all, either mechanical (screen) or chemical (random).
The dithering stems directly from the printing method itself.
By contrast, here are some close-ups at similar resolution (600 dpi) of postcards obviously reproducing paintings (I link to them, so as not to clog the thread with too many big images):
a view of Venice
http://files.myfrogbag.com/qe1mq0/Venezia%20notte%20B%20det%20600-6%20tram.jpg and one of Norway
http://files.myfrogbag.com/qe1mq0/Nge%20fjord%20CFEN%20det%20600-6%20tram.jpg, both using halftone screens; a view of Egypt
http://files.myfrogbag.com/qe1mq0/Memnon%20CPT7364%20det%20600.jpg with random halftoning, which I believe to be a color
collotype http://en.wikipedia.org/wiki/Collotype (I'm not positive about it, I'm not even sure
color collotypes actually exist; what I know is that this process was widely used for B&W postcards, and has excellent random high res halftoning. Scanning at 600 dpi is not enough to get everything out of the best of these cards. The random texture I see in this one is very reminiscent of that).
All three obviously show the original painting technique and texture: they are reproductions.
I hope the difference with the former images is obvious enough.
This is also why I find those so relevant to pixel art - and posted them here: whoever invented this, was thinking and working in a very similar way to us, and found a great creative way to turn their medium restriction(s) into beauty.
Also silly of me, I actually had the answer all along and didn't think of it:
chromolithography http://en.wikipedia.org/wiki/Chromolithography.
Look at the full res first image,
The Old Woman Who Lived in A Shoe, which uses exactly the same dithering technique as my postcards. The other examples shown do not, though.
I have a few of these little naive advertising
chromos, most of them with the same dithering and similar palettes; see one below.
The process is described in the article:
Each color in the image must be separately drawn onto a new stone or plate and applied to the paper one at a time.
What we have here is a direct graphic creation, of something that only exists as art on the final print; and has by nature a limited palette.
This is somewhat different from pointillist
painting: the painter uses pointillism by choice, to the extent that he wishes, remains free to mix whatever colors he wants, and gradually builds the actual piece of art.
An interesting question would be: did pointillism influence chromolithographers?
Did chromolithography influence pointillism?The article dates chromolithography from 1837, although the dithering method was probably introduced much later.
The Old Woman Who Lived in A Shoe is from 1883, the year Seurat started work on his first pointillist important work, according to French Wikipedia
http://fr.wikipedia.org/wiki/Pointillisme (more examples shown than in the English page).
I don't know when those cheap
chromos appeared, but when they did they were just everywhere (exactly like postcards not long afterwards). The pointillist artists must have seen them, and were probably as interested in them as we are, for the same good reasons!
I might post more chromos later.

Btw, I couldn't find a way to link a url to the text, without showing it whole. Is it at all possible?