I did some searching but did not find anyone talking about this. Has anyone added a door switch to a fridge that had none? Any ideas for a switch to use?
I was thinking one of these might be good:
It’s rated for up to 500 mA, I think the Arduino can only do 40 mA on the I/O pins?
Any magnetic “reed switch” like the one LBussy suggests should work as it only needs to complete the circuit.
Or you can simply use tape, aluminum foil and exposed wires.
I hope you will take my reply in the manner in which it was intended when I say that is the least high tech solution ever. 
Hell, I’m sure it works great though.
