A bow saw with a decent blade will cut up to around 5-6" branches, stick to stuff that is lying on the ground with loose bark & not too wet & you should be OK. Wet wood takes a while to dry & moulds/ fungus & wood beetle are not good things to bring into a van with wood furnishings even if it is all MDF really.
If you can afford it a Taylors or Pansy style wall mounted charcoal, coal, or even diesel burner designed for yachts can be very effective without taikng up so much space or effort. Most solid fuel stoves will take different fuels, coal burns hotter & needs a good air flow from below, wood & charcoal work well on a bed of ashes & can be fed air from a draught above the fire bed.
Finding wood is easy when you don't need or want it, but that brilliant unwanted branch by the roadside is usually on a nasty bend with double white lines, a clearway, or nowhere to stop unless you block the lane! If you go for a walk in the woods, you can only gather so much in your arms, you will get very dirty & as already stated, it is theft. Then you have the problem of cutting it up for storage & drying. I suppose you could stash a load on the roof with a net over it, a bit like canal boats do, but it is a bummer to climb the roof in the dark & wet when you need a couple more logs in the night.
Woodburners are a romantic idea, but the reality is graft & mess to achieve the toasty warmth.