There are no high and low pressure fronts, there are high and low pressure areas. The pressure disturbances associated with fronts aren't strong enough for a real effect, you want to look at strong pressure gradients between high and low pressure areas.
At a height of 7 to 8km you are close to the jetstream level meaning your explorers could be exposed to hurricane-force winds, like on Mount Everest. And jetstream-force winds don't just appear around low pressure systems, they can be found in a much wider area. This map shows low pressure at the surface and associated jetstream at 250hPa pressure which is around a height of 10km.
Back to pressure gradients:
Usually pressure in the upper atmosphere is written as the geopotential height of an imaginary plane of constant air pressure, and it is expressed in geopotential dekameters. Like this a pressure gradient can be related to a change of height. If you had a strong low pressure system going "over" your mountain you can have pressure gradients that correspond to a height difference of 500m over the course of 24 hours. That's a very rough estimate though.
You have other problems
A low pressure system can't go "over" your mountain, your mountain is such a major obstacle that it will strongly modify all atmospheric events, I don't really know how a low pressure system would behave if it met with your mountain, my guess is that it would be lead around the mountain by the associated jetstream that would also blow around the mountain then, so that its low-pressure core wouldn't hit the mountain at all. You main problem then will again be the wind. And with the Hurricane-force wind there also comes extreme wind-chill.
Mount Everest was first climbed in the 50s, so if your explorers have 40s equipment it will be hard. Also Mount Everest is surrounded by other mountains that provide additional protection, your volcano is a singular peak, air can flow freely around its flanks. Unless there isn't a stable wind direction so that they can climb in the lee region of the mountain they would have deal with those winds. And passing low pressure systems would mean changes in wind direction and increasing wind speeds.
Even while the pressure gradients are comparable to significant height changes they don't matter much because the associated winds would be the much bigger problem.
If you get pressure gradients, you get winds. If you put your mountain into a calm zone you don't get dangerous winds but also no significant pressure gradients.