ATtiny85: Power consumption vs clock speed
The datasheet shows that current decreases at lower frequencies. Around 1 mA at 1 MHz running at 5 V. More like 5 mA at 8 MHz running at 5 V.



You can save quite a bit by using lower voltages as well, as you can see. For really big savings use a sleep mode. Read about Power saving techniques for microprocessors.



(Edited to add)

To amplify on my remarks, you should be able to get 200 nA consumption at 3.5 V in sleep mode with no watchdog timer. That will still respond to interrupts, such as closing a switch. 





If you need to do things periodically you can enable the watchdog, and then get around 5 µA consumption at 3.5 V.





This is so much less current than the 1 mA mentioned above, that it is well worth exploring running in power-down mode, where possible.