However, I've experienced fog in a wide ranges of temperatures. I like mountaineering and you often get fog high in the mountains. I've been lucky enough to visit the high mountains of Antarctica and I've also experienced fog there at very low temperatures.

This answer (in the comments) and the fog wikipedia article mention that ice fog happens only at extremely low temperatures (-35 or -40 C). But I think I've experienced fog at those temperatures too. Some times, with the right light I've seen the air filled with tiny crystals, but I wouldn't call that fog, because it is very thin.

Then, as far as I can tell, all thick fogs feel and look the same. No matter if they are made out of ice crystals or water droplets. Is that right? Or is there a way to differentiate between ice/water fogs?

Or maybe contrary to what I think, I've never experienced frozen fog.
But: would I notice the difference if I were to ever experience it? How would they feel/look different?

Finally, if somebody also knows why water droplets can stay liquid in clouds down to -30°C, it would be great to learn about that too.

https://www.metoffice.gov.uk/learning/clouds/fog/freezing-fog

The picture below is an ice fog rain bow.

So to conclude Ice equals color and distinct rainbow pattern when it comes to fog.

Diamond dust is what frozen fog is called. https://saebloom.wordpress.com/2016/12/13/diamondsnow/

All the patterns are generated as sunlight (or moonlight) is reflected and refracted in flat six-sided water ice crystals in Earth's atmosphere. https://apod.nasa.gov/apod/ap181221.html

I found this picture of High clouds refracting light. https://www.dkn.tv/tin-giai-tri/nhung-vang-hao-quang-ky-la-tren-bau-troi.html I could get my translator to work but just looking at the picture the sun is past the horizon of the camera but not the clouds and clouds that high is frozen creating a Fire Rainbow.

https://physics.stackexchange.com/questions/289279/why-is-each-snow-flake-different

To add: You could use a telescope and angled white laser or focused light to synthesis a bow to see if it refracts differently between ice/color or liquid/no color and the pattern it makes.

Added After Edit:

http://contrailscience.com/aerodynamic-and-rainbow-contrails/

If the contrail has refraction or rainbow it is ice. The pilot can turn the plane to the angle needed to see the rainbow from the cockpit.

Rain bow at night with spot light. https://atoptics.wordpress.com/2017/02/05/binary-double-rainbows/

If this was ice or fog rather than rain the rainbow will be different in pattern and color. I am interested to try this with the whitest of light or maybe a white laser which does exist.

Last edit: I believe the sunlight is refracted inside the ice and is warmed because of that there must be a equilibrium between the cold air and ice to stay frozen during the day but at night the ice fog could be warmer. I have not considered if the friction between the air and ice as a factor.

这并不是一个完整的答案，但在航空SE的问题“"，答案似乎是:不，他们不能。如果你手头没有飞机，那么所有用来探测冰云的东西似乎都没有用处。没有什么像“翅膀上的光周围有一个特殊的折射模式”之类的。