I have seen a video of a commercial aircraft taking-off with snow on the wings. I wonder how dangerous it is to take-off and fly with snow on the wings.
Pilots are allowed to commence a takeoff if the snow is not adhering to the wing and will blow off during the takeoff roll.
It is very difficult to just look at a snow covered wing and know for sure if the snow will blow off. A "hands on" tactile inspection should be conducted and even then you can never be sure about the level of contamination for the entire wing surface. De-Icing is always the safest option.
To attempt a takeoff with snow and/or ice adhering to the wing is NOT SAFE. You are gambling with your life, and the lives of your passengers and crew.
That being said, it is possible to do a reasonably safe takeoff with snow and/or ice adhering to the wing, but you will need a much longer takeoff roll, and slow rotation, and climb out. If you were to have an engine failure you would probably not have sufficient performance to climb out over obstacles, or even remain airborne.
You are gambling that you have enough runway for your "seat of the pants" takeoff and that you will not have an engine failure, because you have no way of knowing the actual aircraft performance.
So again, De-Icing is the only safe option.
If it's just light snow, it should blow off. If, however, there is ice under that snow, the situation becomes dangerous.
Air Florida Flight 90. It attempted a takeoff with snow and ice on the wings and engine inlets from Washington National, and went into the Potomac River, a combination of inadequate power from the engines, and inadequate lift from the ice encrusted wings. Out of 74 passengers, there were five survivors.
Air Ontario Flight 1363 crashed on takeoff due to ice on the wings, a failure to de-ice after the aircraft had been on the ground at a regional stopover. They couldn't shut the engines down, because the internal APU wasn't working, and couldn't de-ice with the engines running. Bad choice... should have stayed on the ground.
Three years after that, USAir 405 also crashed on takeoff due to ice on the wings, in the same type aircraft: a Fokker F28. In this case, a lengthy delay on the ground while waiting for takeoff let freezing rain build up on the wings.
After USAir 405, deicing procedures and regulations in the US were found to be inadequate, and overhauled.