The video you posted shows the beams themselves very well (with sparkles, no less) so I assume it was snowing steadily when they recorded it. I like the music too, and if this is what they were doing, I can easily imagine it sending lights on the clouds flying rapidly.
The first vid in my post was just a redundant copy of Mick's. My vid contribution was just the famous 2004 original. You can do some fermi-calculations to see what kinds of speeds and illumination are possible.
E.g. assuming the mounts do a sweep from -65 degrees to +65 degrees from vertical (25 degrees to opposite horizons) and back in a second onto a cloud layer at 2km then the average speed of the dot on the cloud will be
? tan(65*Pi/180) (opposite/adjacent) * 2 (triangles) *2 (kilometers) * 2 (per second) * 3600 (seconds per hour)
61761.8 km/h
That's one scary spacecraft! It defies the laws of physics! And that's just the *average* speed.
Similarly, if it loses 0.1% of its brightness every 10m to diffusion, then by the time it's passed through 200 such slices of air/snow (pointing straight up), it will still retain
? 0.999^(2000/10)
0.81865
80+% of its brightness. Each of those 10m slices will be 0.818/0.001 = ~800 times less bright than the dot at the end of it.
Even at the end of the 65 degree throw, where it's passing through 470 10m cylinders of air/snow the final dot has
? 0.999^(2000/cos(65*Pi/180)/10)
0.6228
60+% of the original light (spread out over a wider area, of course), which is still ~600 times more light than any of the 10m slices of air its passed through. Of course, viewing at a close angle to the beam, you'd be looking through many such slices so that ratio would decrease (Mick's , "A) you are at a relative shallow angle to it" from post #4). Hence the low brightness of the beam compared to the dot it produces.
The reason you see the sparkles of the snow in the beam in the vid is because you are so incredibly close to it - as soon as you start positioning yourself many kilometers away from something rather than just tens of metres, everything changes by many orders of magnitude.
Yes, there are some horrific simplifications in the above fag-packet calculations (e.g. cylinder vs. frustum, and my 0.1% loss was pulled out of nowhere - it seems like a highball guess, but snow and mist will be way worse than clean air), but hopefully it's a starting point. Of course, and alas, I'm slowly learning that I'm terrible at explaining things...