I've done the skids course at Brands Hatch amongst others and I've always found ease off the throttle, get the wheels into the turn then slowly open up on the gas and you'll get straight.
That said if you're in a BMW 3-series just give it loads of oversteer and hang it through the corners on the throttle... mind you I'm a nutter and not the best person to ask on these things. Too much time spent watching rallying as a kid

To repeat what the excellent Jeremy Clarkson said not so long ago (few hours ago as I type, in fact) in Top Gear, in a bend rear wheel drive card tend to over-steer and front wheel drive tend to under-steer.

To complete what he said it must be added that at the limits of the envelope, the two kind of cars must be treated differently.

And must be treated differently, in kind, even when loaded differently, but I'm not going there or I'll be writing War and Peace II - the Return of the Cossack, here.

Usually though, when a front wheel drive starts over-steering, like I seem to understand you're wondering, slamming the the throttle close and applying opposite lock only is quite the mistake, because the resistance of the engine braking (which normally is quite useful) will worsen the over-steer no matter how much opposite lock you apply.

I've driven both kind of cars up to the jagged edges of their envelopes and USUALLY when dealing with over-steering front wheel drives (thing that happens mostly because of contaminated tarmac) you should CUT power to the front wheels with the clutch, leaving them to freely spin, and GENTLY apply a degree of opposite lock to recover.

Applying a bit of power instead CAN be as much as useful, but you MUST be able to gauge HOW MUCH POWER to apply, or you will end up only exacerbating the problem and losing control.

This, in fact, poses the problem that if you have an automatic, how you recover is up to the behavior of the gear system. If its clutch releases totally at your cutting the power, you can use the same technique listed above, and if it doesn't (because its advanced system wants to apply engine braking to aid pedal braking, like it is usually done in a manual gear car)... you SHOULD apply a little bit of power, as you hypothesized. The right amount. Which, of course, changes from car to car, from tires to tires, from gear system to gear system, from situation to situation. Just be ready to learn while spinning... which, done in a secure environment, can be quite fun.

Generally speaking, that is.


PS
Never dealt with four wheel drives. Here in south Italy they're the cars of the bombasts, and I'm quite proud not to be one of them.

Remember now, I mentioned winter driving. Going into a slide on black ice is very much different than sliding on pavement or wet pavement. On ice turning your front wheels into the spin is correct. Speaking from experience, and from actually seeing cars around me go into a spin on ice we just keep spinning helpless unless we get slightly proactive with the throttle. So from my experience with front wheel drive, on ice, in a spin, a blanket statement from all the experts that you just turn in and release the throttle is not good advice. The car will only recover when the speed has slowed enough to allow the tires to grab. And you will need very good winter tyres (tires) to recover at higher speeds. I got out of my slide (on ice with front wheel drive) by using moderate amounts of throttle to coax the car into a forward facing position until the tire treads were  facing the direction in which they were meant to face.

Thanks for the comments and keep them coming! Sideways on ice equals very little traction to be compared to Formula racing.   

On my Motor-bike I just stay at home 'till the snow and ice melts...

...or catch a 'Bus!... ...!

Paul...Snow is 'sno joke... ...!

Steve M wrote on Feb 15^th, 2013 at 5:39pm:


All better now. Thanks, Steve!.... ..!

It took more than 4 months for the leg and foot swelling to go down!
It was bloody painful for ages. Luckily nothing broken!

In the meantime, I had to ride my smaller, lighter, Yamaha Motor-Bike, instead of my big Honda.
Motor-Bikes are my only means of transport; (no traffic-jams!), just a problem in snow and ice!

Paul...Motor-Bikes since 1950!...(Defying death!).... ...!

The Painful Reminder...(Motor Bike falling onto leg!)...>>> http://www.simviation.com/phpupload/uploads/1361006442.jpg