First we should see how active noise reduction works. The simplest definition would be:
Active Noise Cancelling uses electric signals to reduce unwanted sounds.
The following picture on Active noise control depicts it in a simple manner:
Then we can see what unwanted sounds ANR can actually reduce. As mentioned in A Guide To Buying An Aviation Headset:
ANR headsets work best at frequencies below about 400-450 Hertz. This
represents the normal frequency range for speech, and also much
propeller and exhaust noise is in this region. ANR headsets are
therefore a significant advantage where intelligibility of
transmissions is affected by engine and propeller noise.
In general, ANR Headsets offer greater hearing protection in
high-noise environments but will do little to reduce noise at higher
frequencies such as wind or airflow noise.
In a flying airplane (even in a slow flight), wind flow would be quite high. This PDF (page 1, paragraph 3) states:
The wind noise spectrum is dominated by the lower frequencies (< 500
Hz), although at 27 mph when saturation is present, the wind noise
level can be greater than 60 dB SPL at 8 kHz.
Since passive noise control is sound reduction by noise-isolating materials such as insulation, sound-absorbing tiles, or a muffler rather than a power source, in an open cockpit, passive NR headsets work better than active NR headsets.