Why the pitot tube is heated but the static port isn't?
Some aircraft DO heat the static port, if only by side effect: Piper PA28 aircraft (Cherokee/Warrior/Archer/Arrow ) for example have the static port located on the pitot mast.  When pitot heat is turned on in these aircraft the entire mast heats up, including the static port.
This characteristic would be the same on most aircraft with a combined pitot/static mast.

As for why most light aircraft don't heat the static port, there are two big reasons.

First, as you've heard, static ports are normally not located in areas susceptible to icing -- they're on the side of the fuselage in areas of relatively undisturbed air (on most of the Cessnas I'm familiar with they're forward of the doors, on other aircraft they're right around where the registration numbers get painted). As Falk pointed out this means ice normally won't accumulate there.
As an additional protection some aircraft have multiple external static ports (connected to a shared static line) so that if one port does get iced over you still have a source of reference pressure.

Second, a static failure is relatively easy to deal with - particularly in unpressurized light aircraft.  Many unpressurized aircraft that are regularly flown in instrument conditions will have an alternate static source in the cabin (which is simply a valve that opens the static line to cabin air), or the traditional "break the VSI glass" solution can be used to get a mostly-working altimeter.