I know you can load up a skin in Paint.net and start painting, but is there a way to visually do it and see the paintbrush on the car in real time as you make the skin?
No, you just have to use the UV maps for reference. You could paste a picture of the car in-game over the UV map on a new layer, then paint on a 3rd layer. You could also use one of the game's default detailed skins, they often use the exact shape of the car.
You also need a Photoshop or GIMP DDS plugin so you can save your paint job as DDS. BeamNG won't load paint jobs that aren't DDS files as far as I'm aware.