You may have diagnosed your own problem - cold damage., especially if the damage is on the side facing the window. But, it could also be an indicator you're overwatering. In winter, and especially when its cold, once a week watering is way too much. That pot is very large for the size cactus (BTW Opuntia microdasys) so will retain moisture for a long time. One of the absolutes to healthy cactus growing is to allow the roots to dry between waterings. The other is adequate light.
