Here are some of the Torr huts a couple of years on from building when the new larch cladding made them stand out like white beacons from the other side of the bay. My untreated sarking boards have mellowed since. The only bit I have treated is the deck at the back which is on the shady side doesn't get much sun and gets very slippery. I'm not sure if I will ever treat the rest with anything. One of the other huts has been painted a rather fetching dark grey and a third with wood stain and contrasting window frames. Others have used clear treatments. One hut site I visited had a rule that if painted the huts had to be green but I think I prefer the dark greys and browns.
Amongst suggestions on face book were linseed oil based preparations, limewashing and Shou sugi ban which involves scorching the wood before its attached.
I don't think I will paint my hut (too lazy and tight-fisted) but they do look nice painted. Attached a picture of a hut at Falkland Estate, that was erected in 2012 and photo taken in 2021, for info. Plain Larch cladding I think. Also a pic of a wee shed I renovated and painted, that I think looks nice. I imagine that painting rough-sawn boards will sook up a lot of paint, so a lot of paint will e needed for the first coat. Should be easier after that.
Best to pick a colour that will not look horrible when it gets the inevitable algae and patina from being outdoors.
Sorry, that's not really very helpful. Just my tuppence worth.