My timber store is in a refurbished outhouse that shares the air with the rest of the house. Timber is thus at the same moisture level as the furniture in the house - generally around 11% +/- 1% through the year.
I have the odd wooden lump in the shed, which I have measured with the moisture meter over the years to find a greater seasonal variation. Perhaps surprisingly, it’s often a bit drier in there than in the house. Physics, though, tells us that cold air generally holds less moisture than warm air, all other things being equal.
I imagine different sheds of various constructions in various locations will see the air’s (and hence the wood’s) moisture levels vary. Being able to keep timber in the same air-moisture conditions as the finished furniture is best, though.
Even some otherwise excellent makers construct their wares in a relatively humid or dry environment so that their stuff can warp or crack when moved into a typical modern house environment - unless the construction techniques are good enough to cater to the relative expansions and contractions induced by moisture level changes.
Personally I don’t mind working in a cool shed. In fact, I find it preferable to a warm shed, especially when planing a lot. If I stored timber in the same place, I’d be more concerned about making sure the moisture levels were similar to those of the furniture’s destination than I would be about the warmth.
