Window insulation in a rented apartment
You can just cover the window with a heat shrinkable window insulation kit such as this one below available at any home store. It will come with the needed tape to affix it to the window frame (from the inside of the apartment) and then all you need is a hair dryer to tighten it up to a nice clean and clear view. Once summer comes again, it will easily remove without any paint damage as the adhesive is similar to a PostIt notepad type system.