I plan to run piping outside and use 1 pump to run my indoor set ups and the ones in the shed.
So, basically, will the pipes that are outside freeze and not work in the winter, if so, are there any solutions to this?
I think you are out of luck. The pipes will freeze and pop, and then when the ice melts and the system runs it will just dribble all over. The only solution would be insulated heated pipes, or find a way to blow the water out with compressed air inbetween mistings.