There are two things to consider - the visa and travel time.
In terms of travel time, you'd be fine. It's roughly an hour in a taxi from SVO to Red Square; the taxi can get you quite close so you'd be able to take a few pics, walk around, and get back to the airport. The taxi ride is about US 30 each way - but try to book ahead because they will try to charge you much more at the airport.
You will need to get a visa to do this, meaning you need an invitation letter from a Russian travel agency. There are companies online that can arrange it for you for a fee. My recent experience was that a friend was not allowed to leave the airport on a transit visa, so I think you'll need to get a tourist one. Cost is typically US $100-$300, depending on how quickly you need it.
So in short - it's do-able, but you'll need to make some arrangements ahead of time!
cheers,
schmare
(from Vladivostok)