Low-power alternative to Arduino, for simple project
The Arduino has regulators and USB-Serial chips that are not Sleep friendly.

If you look at the Datasheet for the ATMega328 (section 32.2.2) however you will see that Sleep states exist down to around 4-8 uA (wake on WDT) for the MCU.

Consider simply building your own Arduino clone (if that's the programming environment you want to use) that has only the ATMega328 (or other AVR such as the ATMega8L) on it. You could run from 3 AAA batteries without a regulator at all providing you don't need to support higher voltage LEDs. 
There are many resources that show how to program an Arduino bootloader environment into a standalone AVR MCU. You could start here and here.