You have some incorrect information. Yes - there are different stallion lines, but ALL haflingers go back to Folie - the one founding stallion. The 7 identifying stallion lines we have now (A, B, N, M, S, ST, W) didn't show up until World War II and actually arose before WWII about wiped out the breed (by the Germans claiming the best horses and taking them back to Germany). Its a German influence that created the lines, but they all originate out of Austria/Italy - not different points in the world.
These stallion lines were supposed to have a "type" to them to help choose a stallion for the mare, but over the years there have been so much cross over between the seven lines that there really aren't too many things to distinguish one line from the other.
In very general terms, A-line tend to be more "modern" and sporty. M-line we tend to joke are the mischevious ones but tend to have some flashy moving buggy horses - especially from Midas Touch. I believe W-line tend to be a little more stocky, old-style but good movers. N-line tend to be a bit more modern but not as well known for it as the A-line.
But these are very big generalities that aren't always true and again - with all the cross over its very rare to find a "pure" line. You are better off looking at the individual stallions within the lines currently available and going from there.
If you go to the www.haflingerhorses.com
website they have a link further down on the page that takes you to pictures of the original stallions of the lines.