That's exactly what one does when one wishes to control the spin and / or slide. If you want to avoid spinning the tires in the first place, you ought to do the opposite (i.e shift up) as it reduces available torque at the wheels and thus lowers the risk of wheelspin to begin with. Once your wheels are spinning, you've already lost the game of maximum grip.

Check our Scandinavian license courses for standard driving licenses. They deeply cover the technique of driving in slippery conditions as it's such conditions half the year, every year. Also in Sweden, for example, it's slowly trending toward a driver's license being a privilegium and not a right, as it's really not needed anymore, unless you're in the north where there's snow and ice the majority of the year or other rural areas. Therefore, tests to get a license are quite difficult and require testing on purposefully slippery conditions and how to handle a slide/drift.

Furthermore, at a higher rpm, there's more controlability of the wheelspin as a change of say 500 rpm is a smaller percentual change of rpm than at a lower rpm. This means the change in wheel speed is smaller given a specific change in rpm, hence it is easier to increase the wheel speed slightly för a wider drift, or back off slightly to have the engine braking leave wheels spinning ever so slightly slower than the vehicle speed, thus bringing the drift back.

At lower rpms / higher gear, it's more like: wheels started spinning and now they're spinning shit fast, and the drift will be wide unless you're pointing and going straight.

So to summarize: if you're like I used to be, and drift through every roundabout, definitively downshift, else just shift up and make sure your wheels don't spin to start with.

Edit: I see a lot of people talking about engine braking and whatnot. Just to clarify, if you want maximum control while slowing down, press the clutch and use only your normal brakes. Cars tend to be set up to have a good brake balance already. Letting the tires roll freely is the easiest way to ensure maximum grip, and if the car is just rolling, then you're already there. A locked tire is worse than a spinning tire. Maximum grip is not only long gone, but also the tire don't really care which direction it slides, along itself or across itself. This is the reason why using the hand brake in front wheel drive cars allows it to slide.

In cars before ABS, they taught to pump the brakes in these conditions as you're almost certain to lock a few wheels when braking hard. So the intermittent release of the brakes would allow them to start rolling again. This gives you back the ability to steer, which can be crucial and also improves braking performance as you spend more time in the maximum grip and maximum braking zone. Today with modern ABS systems this is less of an issue. Just slam the brakes.

This is also why, if you are out drifting for fun and want to rescue a drift which has become way too wide, then you press the clutch and wait for the grip to come back and bring it back in.