Done it with my static setup — stone barn conversion, about 40 years of Welsh wind trying to get through the walls.
Honest answer: yes, but only if you do it properly. Half-measures are worse than nothing because you end up with condensation nightmares. Stone walls are basically giant cold thermal masses that'll cheerfully suck the heat out of any space you try to warm.
What actually worked for me:
- Internal studwork wall with 100mm Rockwool (keep that air gap from the stone!)
- Vapour barrier — don't skip this, seriously
- Insulated the floor before anything else — massive difference
- Decent door seals, because our original ones were basically decorative
Heating-wise I run a small woodburner plus a Victron MultiPlus keeping a bit of background electric heat going overnight from the solar bank. Stone holds warmth reasonably well once you've actually got it up to temperature — that bit is genuinely useful.
The faff factor is real though. Expect a full weekend minimum, probably two. And if your outbuilding is listed or in a conservation area, double-check before you start battering insulation boards everywhere — ask me how I know 😬
What's the size of your space? That changes the calculus quite a bit. Tiny shed-sized thing is a different job to a proper outbuilding.