In my own Brompton experience, when going uphill, unless it is a very sustained climb I think the overall “low” is very slow with those little wheels. I would optimize your higher end gears as that is probably more useful. I do top out on mine currently and then the bike is a little harder to ride without that heavy gear.
I work with bikes and I don’t think the amount of insulation you’d be able to fabricate will increase the ambient temp around the battery to increase efficiency or capacity in any noticeable way.
I think your use case won’t be enough difference any way you cut it. Range extension in freezing temps? Do you reuse all the way through your battery usually?
Your ebike has a larger axle than most bikes so the attachment for the trailer will need to be drilled larger to accommodate. Assuming this ebike is hub drive. If the bike is mid drive then you will probably need a thru axle adapter for your trailer. It’s all pretty much dependent on the rear axle of the bike. Get a name brand trailer like Burley or Copilot. Don’t go blasting around with your kid?? Ha, otherwise ride safely. Trailers can be tricky. Get your bike professionally adjusted and check brakes, wheel fasteners and tire pressure regularly.
TLDR : Duh