The Mini DOES NOT have active notifications. For some reason, they use a different screen. It is a TFT LCD on the Mini vs. AMOLED on the other phones. On an AMOLED, you can only light the pixels you want. On and LCD you have to light the whole screen. Active notifications on an LCD would murder the battery on the Mini.
The Mini has a TFT LCD display, but according to Verizon and hands on reviews from the launch it DOES have active notifications. Active notifications can be run on any type of display, there's an app for something very similar in the Play Store.