Many people and businesses try to claim to be the originator of the "fridge magnet", even going back to Roman times. Advertisements have made their way onto many things, signs, cards, stickers, buttons, playing cards, print ads, postcards, mailings, you name it ads go onto anything that people would see, read, and hopefully keep. The current metal refrigerator is some what recent, before that most "ice boxes" were wooden. Of course with metal parts. So the term "fridge magnets" come about with the introduction of metal refrigerators. If refrigerators turn plastic covered, now being considered, the term may have to change. I am sure a sticky glue from 3M would solve the issue.
Magnet items to attach to other metal things is not new. Even though in the space age, plastic covered magnets seem to claim to be the originator of the "fridge magnets", buttons for may years were made to carry on them political and other ads. It was a simple step to remove the pin and add a magnet to those items. The first recorded American use of a button was for George Washington in 1789. Since then many political organizations use the pin button and more advertisements were placed on pin backed buttons. Although many have tried to claim the invention of the pin backed button too many very old such buttons are found in many museums. Kellogg became famous with the use of free pinback buttons as prizes. Some have collected many unique magnets and are now placed in museums as cultural history.
It was a small step after the 1960's to replace pins with magnets so the button could then be placed on the current metal front refrigerators. Even before that the pins could be pushed into soft surfaces or cloth to display the button and advertisement on them.
Magnets were discovered in ancient times as "loadstone". The Chinese are credited with using it to create the compass but it was until years later the western countries finally studied its properties. Many uses have resulted, the infamous "Fridge Magnet" being just one.
Sample of the many fridge magnets available.