OK, here are a couple tips.
First, after doing home birth I would recommend looking into it. A normal pregnancy isn't a medical condition that needs treatment. Since you might not have experience with the course of events you might want to take a few classes so you don't do something dumb. It wasn't that bad, the midwife monitored vital signs for us and we did the rest.
Tip 1: In cold weather my girlfriend dresses the kid for outdoor play, then wraps the kid in a thick wool blanket on top of that. She figures the kid doesn't really move in the bike carrier seat so needs the extra insulation beyond what the kid needs while running around the playground.
Tip2: In cold rain/snow mix she takes the clear plastic cube thing that covers strollers and puts it over the bike child carrier to keep the winter mix off the kid.
Tip3: That clear plastic stroller cover by "Graco" fits snugly over the Burley single child trailer. She uses the bike child seat more often but sometimes wants to keep stuff in the trailer dry and the stroller cover works.