Actually, mongolian bows are far more suseptable to weather variations, being a highly stressed design held together with water soluble glue. Sinew loves nothing better than to absorb water, losing power, or in extreme cases delaminating with potentially lethal effects. Turkish archers used to heat their bows in special ovens before shooting. Longbow strings were waxed but would stretch if the became saturated with a loss of performance but would still function. The two weapons aren't really comprable. The longbow was a low stress, design that was cheap and easy to produce in large numbers, sacrificing some performance for durability and simplicity. The asiatic composites were all about performance, hang the expense. Kind of like comparing a Lambourgini to a family saloon car.
They were made using fish glue, made by boiling fish swim bladders down. Its very waterproof. Thats why they spent up to 5 days making the glue and applying it( the sinew was coated in this up to a couple of cm thick, along with birch bark which was also covered in the glue)). As the saying goes " nothing good ever comes easy"
To quote the article i posted
As we understand, a composite bow by definition has several layers. We have mentioned the birch frame, and the layer of horn/bone. In addition to this, there is a layer of specially prepared birch bark whose purpose is to protect against penetration of moisture. In addition to this again is a layer of sinew, which is taken from deer, moose or other game animals. The tendons of domestic animals may also be used, but Mongols feel that tendons from wild animals like deer, moose and mountain sheep are the strongest and best. Naturally, the bow has to be glued together. The preferred and traditional substance used for the impregnation of both leather as well as their bows is fish glue. As a matter of fact, fish glue has been proven through millennia to be highly capable of resisting moisture. Moreover, it is durable and lasts longer than modern epoxy resins, which are prone to molecular fatigue. Above all, fish glue is available in all the waters of Siberia where fish is living, among them the greatest of them all, Lake Bajkal.
How is fish glue made? The process that yields the highest quality is to take swim bladders from freshwater fish, soak them into hot water to extract the protein substance, and then boil the resultant soup for a prolonged period. If sufficient quantities of swim bladders cannot be obtained, it is also possible to make hide glue by boiling animal skins. This latter method however results in a glue of inferior quality, because it absorbs moisture, whereas glue made from ichthyic air bladders is highly moisture-resistant.