Yes that is what is happening, if I remember correctly. In the winter season the Northwestern sides block the moist winds coming in from the west which take their moisture from the Mediterranean. The winds hit the North-western end first and precipitate which results in the blue pine, willow and Juniper forests on the slopes, the valleys and the peaks which lay below the tree line. Much the same way the lower Himalays block the southern rains and we get thick pine forests in the Galiyat, Naran, Kaghan, Neelum, Swat, etc. while Gilgit-Baltistan's slopes remain barren, with a few exceptions of course.
In the summers the eastern winds from the Indian Ocean hit the eastern end first and precipitate in the Indus-delta laying at the range's feet (that area is mostly flooded). Both these factors leave the heart of the range dry as a bone. And it is here that we find the pista, cherry, olive, etc. trees on the lower slopes and in the valleys (these trees require less water to survive). This scarcity of rain results in no grass for the better part of the year which makes everything look desolate and barren.
ps: I'm a bit rusty on the Sulaiman and Kirthar ranges, it's been a while since I studied on them.