No, it's better than installing artificial snow to reflect energy.

The snow doesn't change the energy budget of the earth at night, because there is nothing for it to reflect, and the infrared energy it emits is pretty much like the infrared energy from most other surfaces, and a certain percentage makes it off planet and the atmosphere absorbs a certain percentage.

The skypaint emits infrared in a particular bandwidth which the atmosphere does not absorb, called the "atmospheric window", so a much higher portion of it's energy makes it off the planet. This effect will operate regardless of whether the sun is shining on it or not, it will keep dumping something around 120 watts per square meter off the planet as long as it is exposed to the sky.