I want to just clarify that this is for the rear brakes.
The rear backing plate does not do squat for cooling, and it is not easy to replace. The hub must be pressed out of the spindle to slide the backing plate off. The wheel bearing will typically need to be replaced at the same time.
Here are some pictures with the dust shield removed from the backing plate.
http://www.surrealmirage.com/subaru/images/swap/08
I do agree that the dust shield does help keep junk out from behind the rotor, but unless you're driving down dirt roads and doing crazy stuff, you should be fine....even in the snow and rain.
Lastly, if the actual backing plate, not the dust shield is rusted out, it really should be replaced since the caliper bracket mounts to it.
Josh