I think you may be wrong about the roof not leaking, unless you made some repairs on it. You may not see any water from the ceiling because it either sits on top of the ceiling panels or exits inside a wall.
If you do just want to slap a band-aid on it to get through Winter, I'd suggest 6 mil polyethylene and secure that onto the roof with some overhang over the walls. If you get black plastic and have light snowfalls, a lot of what falls may melt and runoff.
An alternative to replacing the rubber membrane is to use a purpose-made roof coating that is similar to truck bed liner. It is more expensive than a new rubber membrane but some folks are having real good luck with the coatings.
roof armor
