“Where was the forward momentum” is a great question.

To create lift, a wing is slightly longer over the top than on the bottom. In normal flight these two layers stay connected to the wings surface. The air on top takes slightly longer creating an area of low pressure. Bernoullis principle in its simplest terms is high pressure moves to low pressure. This is what makes a wing go up or create lift. When the airflow over the airfoil is disrupted by ice, an increased angle of attack is needed to maintain those areas of high and low pressure meaning the airplane nose must pitch up. Pitching up without adding more thrust will result in a slower airspeed. The ice also disrupted the laminar flow causing the smooth air to separate from the wing slightly making it less effective while increasing drag. In icing situations in propellered aircraft you are also losing thrust due to the propeller also being an airfoil. Rough ice reduces the effectiveness of that propellers ability to create a low pressure area in front of it because the laminar flow has been eliminated, and rough turbulent air is now passing on both sides of the airfoil greatly reducing its ability to pull you forward. With that being said it’s unlikely that prop ice contributed as those systems wouldn’t typically both fall at once. It has killed plenty of people in general aviation aircraft without those systems though and they’d usually die in a spin of the same manner.

A flat spin happens when you’ve lost all forward momentum after bleeding off all of your airspeed to the wings critical angle of attack or stall speed and your center of gravity is towards the back of or aft of the aircraft. Normal recovery by pushing forward on the yoke doesn’t work because you are too heavy in the tail. The horizontal stabilizer on the tail is another airfoil and surface that can build ice. It’s basically an upside down wing that creates down pressure. If it’s covered in ice it will get heavy and reduce or eliminate your ability to control pitch. Pair that with your props being accidentally feathered or full of ice and you’ve no longer got anything pulling you forward for thrust and no ability to push your nose over. The momentum left would look a lot like we see in the video. The airplane won’t do anything but fall at that point. The only thing that could be done was to get the propellers making thrust again. Without the tapes we don’t know what was said or tried. We also don’t know if they were hand flying or the autopilot was on. My guess is autopilot was maintaining altitude while they built ice to a point that their speed wasn’t enough to keep it flying. Continuously increasing pitch and losing airspeed due to increased weight. If they meant to drop flaps to increase lift and accidentally took that last remaining thrust away by feathering the props or a single prop an immediate loss of control could develop which is in my best guess what we see happening.

Hope this helps.

Oh, by the way, watch Top Gun! Maverick enters the same type of spin after losing thrust. Probably one of the greatest examples of a flat spin you’ll ever see besides this one.