Is it a feasible idea to run a 3W led via a transistor and a pwm pin...?
It requires a few more parts than that. As Mike says, high-power LEDs (1W or more) are usually run from a special constant-current LED power supply.
These circuits can be tricky to build, and most people just buy the constant-current supply. There are special ICs, or some switching voltage-regulator chips can be used to make a switching current-regulator.
Constant-current supplies normally do use PWM, but there's a bit more to it... There is an inductor to "smooth out" the current from the PWM pulse, and there is feedback "monitoring" the current and adjusting the pulse-width to keep the current constant.
Adding a resistor to this circuit to handle the 1.3V as a load and limit the current to the LED is a common practice.
That's NOT a common practice with high-power LEDs, and it's BAD PRACTICE when most of the voltage (~10V out of 12V) is dropped across the LED. Since LED's are "constant voltage" devices, any changes in power-supply voltage, or in the LED voltage (due to temperature, etc.), will end-up as equal changes across the resistor... For example, if the power supply voltage were to rise by 10%, the voltage across the resistor will almost double! Therefore, the current throught the LED and resistor will also double!
You can get-around that problem by using a higher-voltage supply (maybe 24V), but then the resistor needs to dissipate more than 1W. ...So, the "standard solution" is to use a constant-current switching regulator, which is much more efficient.
A regulated power supply won't vary by 10% (when operating normally), but the point is that the effect of any variations is magnified. And actually, you can often get-away with this stuff in a one-off hobby-project, because you can adjust the resistor value by trial-and-error to compensate for component variations. (That's assuming you don't blow-up too many parts during the trial-and-error testing. ;) )