Can pilots tell if a cloud or fog is made out of water droplets or ice crystals when flying through it?
Boeing provides some decent notes on this in their powerpoint which you can find in full here. Their sections on pilot reports and the summary section have some good notes for identifying ice crystals in flight/clouds/fog 


  
  Pilots have reported rain, sometimes ‘heavy rain’ on the windscreen, Sometimes at impossibly cold temperatures. This is
  believed to be the result of these small ice crystals melting on
  impact with the heated windscreen
  No observations of significant airframe icing
  Turning on landing lights at night and seeing reflective precipitation .It is likely they were seeing the larger particles even
  though they make up a smaller fraction of the population
  Hearing a different sound from rain. Ice crystals hitting the airframe sounded different than rain or hail
  Light to moderate turbulence
  No significant airframe icing
  TAT probe frozen
  Ice detector not detecting ice (when installed)
  Appearance of rain on the windshield
  


The same powerpoint also discusses that satellite imagery can be used to see ice crystals. A lot of planes even small stuff have the ability to receive feeds of this data which can be used to identify sections of ice crystals in flight. 

According to various sources the threat is particularly dangerous due to the fact that there is no hard and vast way to visually identify the crystals and in many cases the effects are similar to other events and may lead the pilot to belive something else is happening.

For pilots we can only go by look, unless you are flying slow in a 172 you cant exactly pop the window open at altitude and feel the cloud. Simply put pilots can not reasonably tell if a cloud is vapor or crystal prior to flying into it and observing the above noted actions.