My son’s not quite 2 and a half, I use a Yepp Maxi seat on an Xtracycle Free Radical (search the forum for previous posts on kid carrying, Stoner has the same set-up and has posted pics).
I carry his rucksack on my back, my bag (pannier) on the back, plus I usually have his scooter or balance bike strapped on behind the Yepp seat.
I also have a trailer, but never liked it. It doesn’t weigh that much but adds a huge ‘drag’ feeling to the bike, like I’m towing way more weight than I actually am. Having the boy on the bike still feels heavy, but way, way easier than the trailer. I also don’t like the width of the trailer, I feel like cars are more likely to hit it than just the bike, as they have to pull out more. I know you could argue that it’s similar to owning the lane, but I just don’t like it. plus there’s storage of the trailer – can you leave it at the daycare? Can you store it at work?
As for weather… we cycle every day, regardless of the weather. It never snows here but does get down to 1 or 2 degrees C, so chilly enough for a kid on the back. For the wet/cold days he just has a waterproof all-in-one suit with an appropriate amount of layers underneath, and wellies on with the suit legs over the top which are effectively water- and draft-proof. Hood up, helmet over the top, toasty as. Sunnies on all year round, they keep the sun and rain out. He’s never complained about the wind, cold or rain.