To be honest, a lot of it is porting IRL stuff over . . .
So for instance, a unit that is designated as 'Mountain' (in the US, its the
https://en.wikipedia.org/wiki/10th_Mountain_Division) specifically and frequently trains in mountainous areas so that the troops assigned to that unit build familiarity with the nature of combat in mountainous areas. So yes for BT, that means you are more likely to get jump capable mechs and tracked vehicles over hover and to a lesser extent wheeled. Infantry might be more likely to be jump infantry and travel on VTOLs rather than ground bound APCs- likely they really took to BA when introduced. Mountain-qualified heavy equipment maybe more portable or easier to break down (thus a cost modifier over general issue)- some of it might even be able to be broken down for individual carry (
https://en.wikipedia.org/wiki/Gebirgsflak_38- general purpose AA & field gun) to get over the roughest terrain. In BT they might even be trained to use supplemental oxygen for conditions like the Himalayas or other mountains that scratch the edge of atmo. Mountain specialized troops will also have IMO better cold weather gear than the average trooper- for instance I when I was in we had a 4 part sleeping system (b/c it could never be called a sleeping bag). We were only issued 2 or 3 parts IIRC b/c the final part was for arctic/mountain conditions. Some nations mountain/arctic troops were also issued skis or snowshoes to increase the infantry's mobility but I am not sure that would carry over to BT though since we do have beast mounted troops . . . Some mountain troops were also issued pack mules to be able to carry a squad/platoon/company's logistics since they were going places trucks could not go- and VTOL airlift is not always possible.
Imagine trying to resupply this place in a storm-
While regular troops w/o the specialization could fight in those conditions, they will not be equipped or physically conditioned to operate in that environment as well as mountain troops. Commanders and staff will not be as familiar with the needs/requirements of fighting in those conditions which means they will likely suffer more non-combat injuries (frostbite for sentries for example) and when in combat they will be unable to exploit any opportunities to the same degree mountain troops would- even if the equipment issue to individuals would be the same.