What prevents cold air from coming in through evaporative cooler
The evaporative coolers that sit on roof are normally serviced in the fall at the end of the usage season. Typical service includes shutting off the water supply to the cooler, draining the water sump in the cooler, cleaning away any debris and leaves that may have accumulated around the unit and then installing a cover over the whole cooler shroud. The jacket may be a canvas or tight wave synthetic fabric material. 

These covers are typically available at home centers and evaporative cooler suppliers and have to be purchased by size. They are typically sewn as a fitted cover that then has a closure along one side that is cinched up with heavy cord similar to lacing a shoe. Some covers have a draw string in a hem around the bottom that allows the cover to be cinched down under the lower edge of the cooler shroud to prevent it from being blown off in strong winds.

Since evaporative coolers are typically used in areas where there is intense sun for large parts of the year be prepared to have to replace the cooler cover every few years.