Efficient periodic wake up for sensor reads
Please refer to http://playground.arduino.cc/Learning/ArduinoSleepCode

it explains the details of a the sleep command and interrupts to re-a-wake. Where the power savings is from putting the resources individually into low power mode.

In your solution, you may want to put everything in low power, except power_timer1_disable(). Where timer1 would be configured to provide an overflow interrupt, say every 1 minute or longer and then go back to powering all off and return to sleep.

Note the article also mentions that the UNO's power supply is a linear regulator, which is very in-efficient. You may want to use your own. You can also get away with just running directly off of 2-3 AA's, if your other circuitry does not care. If this, then I would also suggest enabling the brown out detection, to ensure low battery does not get funny.