the missing door-seal will actually let in quite a lot of humid air which would cause the frosting over of the evaporator coils you see, also it would cause the thermostat to never shut off, which again would lead to frosting over of the coils. ( because the evaporator would never have time to defrost between on/off cycles)
even with the evaporator fan running, once the coils plug-up with frost, it snowballs from there ...
(HAA!!! bad pun!)