From december 23 - january 1 one week before the examination period (january 8), the amount of available study spots is about 100 spots for the entire university. Moreover, all the available study spots are located on KTH Campus Valhallavägen, and thus zero study spots are available in e.g. Kista, Södertälje and Flemingsberg.
For more info from KTH regarding winter opening hours:
https://www.kth.se/en/student/kontakt/campus/oppettider-under-julen-1.1210295