I did some more reading and I found some more data but I don't know that it is more information
From the datasheet
17.3 External Clock Source
An external clock source applied to the T1/T0 pin can be used as Timer/Counter clock (clkT1/clkT0). The T1/T0 pin is sampled once every system clock cycle by the pin synchronization logic.
This makes is sound like you can not "Power Down" but you may be able to go into "Stand-By" where the clock keeps running.
T0 is used to clock the Timer 0 and since that is used for "delay()", "millis()" and such. I don't think that is a good option.
14.3.3 Alternate Functions of Port D
T1 (Timer/Counter 1 External Counter Input)
OC0B (Timer/Counter0 Output Compare Match B Output)
PCINT21 (Pin Change Interrupt 21)
I don't know which pin that is on the Arduino.
• T1/OC0B/PCINT21 – Port D, Bit 5
T1, Timer/Counter1 counter source.
OC0B, Output Compare Match output: The PD5 pin can serve as an external output for the Timer/Counter0 Compare Match B. The PD5 pin has to be configured as an output (DDD5 set (one)) to serve this function. The OC0B pin is also the output pin for the PWM mode timer function.
PCINT21: Pin Change Interrupt source 21. The PD5 pin can serve as an external interrupt source.
16.11.2 TCCR1B – Timer/Counter1 Control Register B
• Bit 2:0 – CS12:0: Clock Select
The three Clock Select bits select the clock source to be used by the Timer/Counter, see Figure 16-10 and Figure 16-11.
It looks like you can select the external clock just like you would select a prescaled clock.
Now, since Counter 1 is a 16 bit counter, you should be able to set a threshold of up to 65536 seconds or over 18 hours.
There may be a lot of reason this won't work. I may be totally wrong in my reading of the datasheet, and I am still learning but I thought I would like learn why this wouldn't work.