Are passive or active headsets preferable in an open cockpit? My first headset used passive noise reduction (i.e. padding) and when I - very quickly - upgraded to an ANR headset, my instructor recommended keeping the passive one "in case you ever fly something with an open cockpit". I can't remember if he gave me an explanation, but he definitely said that passive headsets "worked better" in an open cockpit.

I haven't flown anything open so I've never had the chance to put this to the test, but is it (or was it ever) true?
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 (&lt; 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.