Why does the brake pedal on a Volvo 850 turbo go hard when coasting downhill in 'Drive' gear?

"because its gay"Okay... that is NOT why...

Simply put, most likely the brake booster is losing its vacuum for whatever reason.

On a turbo, this could be caused by lower intake vacuum as a result of high back-pressure from the idling turbo - which could be caused by a failing turbo or pressure regulator. Checking for boosting on lower-than-expected-loads would tell you if the boost regulator is to blame. Checking the turbo back-pressure is trickier, but you should notice lower fuel economy at lower loads.

However, you really should check the simple things first:

Jack the back of the car up as high as you can while it is running... check for vacuum problems at the brake booster - it is possible there is water in the line preventing vacuum from building up.

My Volvo 850 does this sometimes as well... and it is not a turbo.

Lastly, you could have the beginning of a brake booster failure as well... but then you should notice a hard pedal more often.. not just when going downhill.