A RTC will be the best solution, or a 32kHz (watch) crystal for the T2 timer/counter.
Power consumption depends on Vcc, and also is almost proportional to the CPU clock frequency. The oscillator frequency (16MHz) can be divided by the clock prescaler, so that the controller will not run faster than required for your project.
When you select a sleep mode during inactive periods, an Arduino clock must keep running for counting cycles, and the controller has to wake up with every counter overflow. This can be achieved with power-save mode, where T2 continues running. Entering sleep modes have been discussed frequently in this forum.