If you use the design concept that a lot of wireless door bells use you can reduce the power consumption
but not eliminate it.
A pair of AA batteries will run a 433 Mhz receiver drawing 4 ma for around 1 month.
If you use Alkaline C batteries , around 8000 mah , you can get around 2 1/2 months.
Doorbells simply use a 433 Mhz receiver and a Cmos data decoder like a PT2272/ SC 2272.http://www.adafruit.com/datasheets/PT2272.pdf
For a simple off / on application, this is all thats needed.
The Decoder simply provides 4 bits of data which can be used to turn things on and off.
Using a encoder like a PT2262 / SC 2262 , to provide the transmitted data to the 433 Mhz transmitter is all
The decoder chip being Cmos, only draws around 20 ua.
You dont need an Arduino at all, which reduces drastically the power consumption.