Two things happen that cause the warning lights to go out. The oil pressure light ground circuit is through the sensor. A little pressure, light goes out.

The other lights ground through the alternator brushes. When the alternator spins up and starts charging, the lights go out.

Your situation sounds like the alternator is slow in getting up to output. Have you checked or replaced the brushes? They will eventually wear out, and the shorted they get, the more likely they are to produce weird effects.

Cold day, short brushes? Brush springs have to push farther out, and there may be some cold sticky oily stuff in the brush channel. Slow in getting good contact. Warm engine removes the stickiness.

Easy fix. Post if you need more info.

Good Luck,

Bob

:>)