Is this original upholstery on a Moller chair Hallingdal or something else?  

try a product called Folex
it is magic.

I've seen a lot of Møllers with
a wool that looks sort of like Hallingdal but not really. (Your photo isn't showing up at the moment so I'm not sure about yours.)
Hallingdal has threads of the same thickness crosswise and lengthwise.
The fabric I've seen on Møllers has two different thicknesses of threads and I think a double strand in one direction, maybe. It is nice fabric but I don't think it's as durable as Hallingdal. It seems softer and a little thinner.

Thank you both.
OK, so then it's not Hallingdal since the threads are not of the same thickness, I don't think. The fabric is sort of nubby.
Spanky, I know you've restored many Mollers. May I ask what you do to clean small spots on the upholstery? Do you know the Folex product as well?

Nope, not Hallingdal--
the yarns form squares on Hallingdal and there isn't any space in between them.
I have never used Folex. Somewhere on here there's a discussion of how to clean wool upholstery. I have used dish detergent suds with some success but a waterless wool wash might be a better bet. Maybe that's what Folex is? There's also one called Eucalan that is supposed to be really good. You don't have to rinse it. I'm not sure how it works but one of these days I'm going to get some and try it. People buy it for very high quality hand-knit sweaters.
Here's some Hallingdal just for reference's sake (for others reading this now and later).

Thanks!
I actually have some Eucalan on hand, it's good stuff. I use it to wash my vintage flokati rug (which, incidentally, can be done in a washing machine.) I don't know why it didn't occur to me to give it a try... good idea. I do think the fabric is wool, or mostly wool, so it should be appropriate.