Why do LED headlamp bulbs need active cooling?
Here's an interesting video comparing a 25/25W LED headlight to a 90/100W halogen.

Philips Luxeon H4 Headlight Temperature Output vs Halogen

The passive heatsink at the rear of the LED lamp got up to 74 °C, while the halogen lamp reached 99 °C at the bulb holder. Considering the difference in power consumption, the temperature difference doesn't seem that much! 

The halogen lamp's quartz bulb has to reach a surface temperature of 250 °C in order to maintain the halogen cycle, and the filament inside runs at ~3000 °C, so why doesn't the outside of the lamp get a lot hotter? One answer can be guessed from the measurements at the front of the lamps. The LED lamp only got up to 33 °C, but the Halogen measured 60 °C. 

An LED only emits visible light, so most of the heat produced has to be dissipated by the heatsink. A halogen lamp dissipates a lot of heat too, but it also emits infrared light directly out the front along with the visible light. Some of that infrared is absorbed by the front glass, but a lot of it passes through and so does not heat up the lamp.

In the graph below we see that a halogen lamp emits much more infrared than visible light. If that light was useful to us the lamp would be considered far more efficient.

Halogen Lamp Spectrum


The other difference is that halogen lamps are designed to run hot (which they must to work properly), but LEDs are less efficient at high temperature and may be damaged by going over 150 °C, so they need better heat sinking.