> Um, no, the brakes don't do the same - if you have disc brakes, the
> brakes stop the wheels when fully engaged

Of course, because through the brakes you are applying more torque than the 
tyre/road surface can provide, so the wheel locks.

> Conversely, by downshifting, you increase the
> engine revs and the wheels are not locked - they still turn.

Only because *usually* the negative torque applied from the engine is not 
enough to overcome the grip between the tyre/road.  Try downshifting on ice 
or even on wet tarmac violently (eg 4th to 2nd at 40mph) and you will lock 
the wheels (certainly audible on wet/dry tarmac).

BTW the two effects add up, so if you are already braking hard with the 
pedal, downshifting hard at the same time will likely lock the wheels 
easily, this is why racing drivers always "blip" the throttle while braking 
and changing down, to avoid the engine braking that could lock the wheels.

> Now, when you're on dry pavement, the wheels normally don't lock because
> the car's momentum overcomes the friction on the brakes, bringing you to
> a gentle (or sometimes less-than-gentle) stop.  On ice, though, it takes
> less friction of the brake pads against the wheel to stop the wheels
> because it takes less to overcome the friction of the wheel against the
> ground.
>
> So it's easier to lock the wheels up and skid.

Yes, and the same applies to engine braking.  Next time it's wet or snowy 
try changing down (a couple of) gear(s) and letting the clutch out quickly, 
you'll hear/feel the driven wheels lock until the car slows enough for the 
wheels to grip again.  Obviously on snow and ice this happens easier.

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