hey, I was just playing around with this; I know this is an old thread, but if someone else is searching...
The 1999 Skyhawk Cessna 172 I'm flying in the real world has fuel injection (so no carb heat). It does, however, have "Intake Heat" (labeled "alternate air").
So I cranked up the icing in FSX on the weather page, flying the default Cessna 172, and pulled the "Alternate Air" knob; just like the OP, no good, it's the alternate static air knob, not the intake heat! I started sinking as the RPMs started dropping!
I searched all over for the knob/lever/anything related to carb heat/alternate air; but found nothing.
PRESS H!!!! Press the letter "H", and even though you don't have a visible control, it still seems to work! I tried it, and when I press H, the RPMs slowly come back and control is regained. If I press H again (turning it back off), I again lose RPMs until the plane is coming down out of the sky.
So you do have that feature, it's just invisible!