Icing is caused by supercooled raindrops freezing on the airframe. In this case the spacecraft came from a very high altitude so I'd expect the airframe to already be very cold and even if droplets aren't supercooled, they might just freeze on the cold surface of the lens. Pireps (pilot reports) are available globally where pilots report icing conditions they encounter. I suspect the SpaceX engineers anticipated this possibility and decided that they didn't want to add the extra weight and complexity of a heating or deicing system to the lens.

I have a feeling someone is working there right now to come up with a quick and dirty deicing system - considering how disappointing this video is. The fluid system the Cirrus SR22 uses comes to mind.

I think some kind of disposable multi-layered lens cover that peels off automatically would work well. Pretty cheap, and easily replaceable. Effective against more than just ice.

I propose a revolutionary solution: a lens cap.

I'm assuming that they only need the video from when they get close to landing so the lens cap can be ejected once the rocket is low enough in the atmosphere that icing is not a problem.

or some kind of heating element would work, too.

I speculate that this one iced up because the vehicle flew a much higher trajectory than the previous vehicle, as visually noticed from the launch webcast. This meant that the first stage spent more time higher in the atmosphere.

I was wondering that as well. Three possibilities come to mind;

1) Atmospheric conditions are right for it (flying a subzero steel device through clouds with moisture in them, same problem that airplanes have)

2) The burning of the cryo-propellants lead to additional ice formation (as they burn they expand from liquid to gas and pull heat out of the tanks/body)

3) "snow" which is a variation on #2 which is that ice crystals that are forming on the rocket as it burns propellant in ascent the camera is accelerating away from them, but in descent the crystals are coming towards the camera.

Either way its an 'easy' fix, whether you heat the cover, add a wiper (ala nascar) or change the position.

No, it wasn't clouds - it passed through a chemtrail.

For all the rocket science, why can't they get a lens that deices itself?

They will. It's not been seen to be a problem before, so they went with the simplest solution. In rockets, every ounce counts. Now they know it happens (at least sometimes) in this very novel flight regime, they'll do something about it--the linked post even says so explicitly.