I got to thinking about the vulnerability to moisture of the glues used for Medieval compound bows.
One account of a record long range shot by an English archer using a Turkish bow mentioned that the bow was very old and before shooting with it the owner had spent some time rehydrating the bow and drawing it progressively till certain it wouldn't fail.
This suggests the bow had been stored in a dry environment, perhaps a collection in a building that was well heated in the winter or whenever rain was a problem.
Ordinarily very cold winter air has less moisture than warm air, only when ice and snow melt would moisture laden air be a problem.
In spring and summer torential rains would drive up humidity.
Composite crossbow prods appear to have failed only if exposed to extended rain without an effective case or covering, which was not feasible when going into battle, and even then accounts say that they lost power and range not that they failed completely.
The English Bowmen had effective bow cases to protect their bows and self bows were less affected by moisture as long as bow strings were kept dry. Spare strings have been mentioned as well.
Companies of Arab archers were hired as mercenaries in a number of European conflicts. They apparently knew how to avoid moisture damage to their bows.
Composite horn hunting bows used in northern climes such as parts of Russia are known from archaeological finds.
These were found to be tightly wrapped with thin bark which may have kept out moisture to some extent.
The Esikimo also used powerful composite bows of very different construction , mainly because proper bow woods were not to be found that far north.
Steel bows were mentioned earlier.
Steel isn't very efficient for bows of heavier draw weights, as the diminish returns of heavy draw steel crossbows has proven, but seems to work well for lighter target and hunting bows. The quality of the steel is a factor but various methods of improving the cast, such as grooved or hollowed limbs, are displayed in surviving examples.
The Indian steel bows kept in aresenals were inferior in cast even to self wood bows but could be stored for decades without degradation. Composite and to a lesser extent self bows require good storage conditions and hands on inspection and upkeep to remain trustworthy battle weapons when stored for extended periods.
I have seen an Indian war bow described as being made from whale bone, possibly Baleen as used in corset stays, and steel, but haven't found any information on details of construction.