Historical trekking is essentially a camping trip done with clothing and equipment that is historically correct for the period you are emulating. The thing that differentiates historical trekking from the sort of camping done at rendezvous and reenactments is movement. At a rendezvous, you live in a stationary camp at the event, but a trek implies travel, usually on foot, though trekking can also be done by canoe or on horseback. However you do it, it is the movement that makes it a trek.
It’s the element of travel that makes a big impact on the gear you’ll use. When I camp at a big event, I like my comfort. I’ll have a tent, an awning, a cot with three fluffy wool blankets, candle lanterns, cast-iron cooking gear, clean clothes…
