Yes, I've done many (used to be Director of a timber frame company that manufactured them).
Timber frame insulated with PIR (Kingspan/Celotex) insulation is the way to go, but you need to decide how far you want to go with longevity vs. cost.
On a 'proper' timber frame construction, you have a ventilated gap behind the external cladding, then a 'breather membrane' (basically a breathable waterproof fabric) on the outer face of the sheathing on the timber frame itself.
Then on the inside of the timber frame, you have a sheet of polythene, called the 'vapour barrier', whose job is to stop any moisture from the warm air inside the building from getting into the wall structure, where it cools down and the moisture condenses out, causing the timber frame to rot.
The extra complication of doing it properly increases the cost substantially, so you need to decide whether it's worth it for you, or whether you're happy to simply accept that the building will have a limited lifespan.
You need to avoid the need for Building Regulations compliance, which means keeping the floor area below 30m2 (so 6x4m. is fine) and at least 1m. from any boundary (otherwise there are complications with using timber cladding, due to fire risk). If Building Regulations kick in, you've got problems... not only will they expect compliance with fire regulations and the moisture-proof construction described above, they'll also require structural calculations to prove that the timber frame is adequate.
If you can, you also need to avoid the need for Planning permission, by sticking to the rules on 'Permitted Development'.
Cost is a piece of string, but depending on design and construction quality, and how much work you put in yourself, could run anywhere from £3k to £30K.