Warm milk has a slight edge. While there is no direct head-to-head study comparing the two, warm liquids in general have a greater calming effect on the nervous system than cold ones. The warmth also signals your body to slow down, making it a stronger sleep trigger.
Cold milk still delivers the same nutrients (tryptophan, magnesium, calcium) — so if you strongly prefer cold milk, you will still get the nutritional benefits. The difference is mostly in the psychological and relaxation effect.