If you do an internet search on "frozen seed bank" you will find all kinds of resources, including the most famous: the Svalbard Vault. The bottom line is that seeds stored at zero degrees fahrenheit will remain viable for at least 50 years. Further lowering the tempertature, lowering the oxygen content and lowering the humidity will all add more decades to how long seeds can be maintained.

The sources also say that seeds stored in a common refrigerator at 35-40 degrees fahrenheit will remain viable for at least 20 years, so I'd have to say you are in luck. Give it a whirl!