Houdini's fireworks have an inherit color, which is the attribute called Cd. This needs to be passed the Arnold shader network to be used.
Under the attached Arnold properties is a tab called Attributes. Clicking the down arrow next to Point Attributes will list the available attributes on the fireworks, choose Cd. This will pass the attribute to the .ass file as User Data.
Now go the shop and into the fireworks vopnet. Create a User Data RGB node and attach it to the Emission Color of the Standard Surface Surface shader.
Select the user_data_rgb1 node and type Cd in Attribute.
Now the disks should be rendered with color.
Turning The Particles Into Volumes
At the moment the Particles are being rendered as flat colored disks but they could be rendered as spheres with volume.
Select the fireworks and go to the Shapes properties again. To turn on volumes the Volume Step Size needs to be increased to 0.02 and the Mode set to Sphere.
Now go the fireworks vopnet and delete the Standard Surface shader. Create a Volume Collector node instead. Attach it to the volume parameter of the OUT_material. Connect the user_data_rgb1 to the emission of the volume_collector1.
Render the scene again.
It is very dull because the values being passed to the volume_collector1 are very low. Insert a Multiply node and set Input2 to 40.
Close up, the volumetric nature of the spheres can be seen.
The resulting scene from this section can be downloaded below.