You wouldn't put a plastic bag over your babies head - would you? Use a green garbage bag just to keep him dry? Perhaps to keep the wind off him or maybe the germs away?
I thought not. It seems absurd, doesn't it ?
So why would you cover your stroller with a sturdy plastic cover and lash it in place? I know he appears to be sleeping soundly but appears may be the operative word. That cover may well be trapping the CO2 he is breathing out and perhaps that is not a naturally induced sleep rather lethargy induced by the lack of oxygen in his little cocoon. Co2 is heavy and will settle around him trapped by the stroller hood and with no flow of air due to the plastic cover you've left in place to create his little bubble you may be causing brain damage in your efforts to keep him safe. Always choose a cover that allows for adequate air flow. There should be an opening at the top and the bottom should be loose or open. And if he gets a little wet believe me when I say he'll be fine !