Solution to interrupt Arduino every n seconds
So, since you're coming from the application domain there are some things you might want to consider:


Make sure to always stay inside the super loop. With an Arduino or any other Microcontroller (not using a RTOS) you do not have anything defined that's going to happen after the superloop. Everything that happens after this loop is basically undefined (it typically is a reboot or jump to a default interrupt handler but may also be a lockup). Simply telling the processor to "exit" will .. well, exit - but you have no idea where it's going after that. To allow for interrupts and further execution of your main code, you need to have your processor in a defined state (and that basically is the super-loop). as a comparison with your PC, after you exit a thread, the operating system will take over. On your Arduino there is no such concept. The super-loop IS your OS (well, at least it's some minimum implementation of a non-preemptive scheduler).
If you want to have only interrupt actions active while the processor is using only little power, you will need to use the processors sleep modes. These are modes, where special functionality is disabled but which keeps the processor alive or in some idle mode where it's actually just waiting. Whilst the Arduino may have various sleep modes, none of them are what can be achieved with other architectures, such as the MSP430 platform or some SAMxL platform. Those are dedicated as low power processor and provide the necessary deep sleep modes.
When using a deep sleep mode, it depends on the actual sleep mode which interrupts can wake the processor. Typically for the deepest sleep modes, only few interrupt sources will actually wake the processor up as all other peripherals are inactive either because their clock was gated or power was turned off for that function block.
You will always have some power drain for the processor but keep in mind that it's not only the processor which will require power. At some point, you have leakage currents through your capacitors/resistors and other ICs on your board which require power as well. When you're talking about "years", you will also need to account for the battery discharge as well. No battery is perfect.
Jack Ganssle is probably well known for his insight into anything related embedded, but he explicitly wrote some articles for ultra-low-power systems. You must read those if you want to start somewhere. While having the software side covered using low power techniques you will also need to tackle the hardware side, yet as I said - the Arduino wasn't made for such tasks even if it provides some basic sleep modes.