Did they march around with some sort of protected fire that had to be quickly distributed? Or, did individual soldiers have a way to quickly get fires going to light their weapons?
The "match" in matchlock refers to the lengthy matchcord, consisting of cord infused with sulphur and other flammable substances that would slowly burn, much like a fuse, providing you with ready source of ignition.
So yes, they did exactly that, by dint of the matchcord being the primary way to set off their weapon. I found one reference to 4 feet or about a yard of matchcord for soldiers, but I don't know for how long a period that would last. While I made reference to a fuse that's not to be taken as a suggestion they burn as fast, it's *very* slow burning, that's the whole point. The soldier could keep it coiled around an arm and tuck it under protective clothing in inclement weather.
On a march not all soldiers would have it lit to save on matchcord, but you could get a light from your fellow soldiers. I've tried to look and even though I think I've seen numbers mentioned for how large a fraction of soldiers would have lit cords I can't find it now.
While the matchcord naturally is fairly cumbersome it was a step up from the earlier handguns where you had to apply a hot metal stick to the touch-hole. These earlier types would necessitate a brazier for the soldiers, needless to say you'd not want to be them surprised on the march. Though in fairness, at the time handgunners were still a small expert part of the army. The refinement of the handgun in 1450-70 with a lock, serpentine lever and trigger mechanism was a clear step up, though being a matchlock gunner guarding the artillery and gunpowder store was still a job for careful people...
It's probably not surprising that the first matchcord free weapons, the primitive flintlocks, known as firelocks sometimes, where distributed to sentries (where the glow of the cord didn't give their position away and they could more quickly fire without blowing on the cord to get it going properly) and artillery guards first.
While on the subject, the wheellock could of course also be used in such situations, but it was an intricate and thus expensive mechanism so tended to be only be found in high-end weapons. It was also delicate, so naturally too fragile do give to the average soldier... It was mostly used as a mechanism, for pistols, a speciality weapon for the mounted arms or officers.
Constantly having matchcords burning was also wasteful and a considerable expense for armies, so there were many benefits of moving to the flintlock type when it was invented. You could also retrofit matchlock muskets to flintlocks so it didn't take long after the introduction until matchlocks were phased out in the last decades of the 1600s.