Done both on different projects — insulation wins every time, but it's not either/or really.
Stone has terrible thermal mass behaviour in cold climates. It sucks heat out of a space for hours before it starts giving anything back. A wood burner into an uninsulated bothy is basically heating the walls indefinitely. Inefficient and you'll burn through a serious amount of wood.
On my tiny house build I used 50mm PIR board (Celotex GA4000) against the walls before battening out. Transformative. Same principle applies to a bothy — even a basic 25mm layer with a vapour barrier makes a massive difference to how quickly the space gets up to temperature and how long it holds it.
Practical order I'd suggest:
- Tackle the floor first — cold floors kill warmth faster than anything
- Ceiling/roof void — heat rises, obvious losses there
- Walls — even partial coverage helps
- Then fit the wood burner
The stone walls themselves aren't going anywhere so you're not fighting them, you're just lining the inside. Rockwool between battens works fine if PIR feels like overkill for a bothy.
One thing worth flagging — moisture. Stone buildings trap damp badly if you seal them without thinking about breathability. Make sure whatever system you use accounts for that or you'll have a mould problem by spring.
What's the bothy footprint roughly? And is it a weekend-use situation or longer stays? That'd change how much effort is genuinely worth it.