It appears that images of these huts occur with some frequency in the background landscapes of medieval illustrations, mainly those showing Angels announcing the birth of Christ. They take different forms, but they're often just a square wooden shed with 2 or 4 wheels attached. Presumably they were pushed or hitched, as flocks were moved about in the open countryside (enclosed sheep fields were a 16th century creation) and as a place for shepherds to take refuge and probably sleep in.
So making one seems both relatively easy and something which would add a little interest in a corner of a wargames table- those areas where you rarely get any gaming happening and so need a little terrain item to be placed.
A recent order from Charlie Foxtrot Models enables me to add their Derelict Shed, as I didn't want it to look too much like a modern garden hut. This was made as it comes, apart from leaving off the door. Wheels are also mdf from 4Ground and the tiles are left over wooden shingles from an AWI build. It looks a little like a Regency period bathing hut, doesn't it!
So a quick, mobile terrain item which I should be able to use on any medieval game - however, I've realised that I have no sheep!!