What languages did they speak in Kashmir over the centuries?

Devimahatmya manuscript on palm-leaf, in an early Bhujimol script, Bihar or Nepal, 11th century

It seems to have been mostly Persian with some Turkish, and here is where I got that data from:

Linguistic history of the Indian subcontinent
Indo-European languages
Confessions of a Linguist!
Steve Huffman Language map
Timur & Timurid Architecture
Linguistic history of the Indian subcontinent