Are replacement MTB tire studs compatible between brands
This article measures the sizes of studs between manufacturers. The upshot of the article is that if you have Nokian, Schwalbe, Continental, Innova studs, the dimensions are essentially the same and can be swapped around. 

In any case, I'd expect Nokian (Suomi) studs to be the easiest ones to find these days anyway... 

For reference, the essential from teh article linked above is that the studs are approximately:
"Overall height: 5.8mm (pointed), and 5.5mm (domed)

Base height: 1.0mm

Base diameter: 6.5mm

Shaft diameter: 3.4mm

Tip diameter: 2.0mm"