I don't think it's the cold temp, just the physical activity. For us it actually happens more when it's hot, because he sweats more and loses fluids, so needs to drink constantly. It also happened once when we went sledding in the winter.
But I am no expert, just recounting our experience.
could you explain "dipped his urine...no protein/keytones.."? How and why do you do this? My son was just diagnosed a few weeks ago and I am trying to learn as much as I can. He will be 3 at the end of the summer. Thanks!