Experience biking with child trailer during winter? What's your experience biking with child trailer during winter in the city? 

I live in Cracow, Poland. Recent winters were almost snow-less, but it's &lt;0°C cold and slippery anyway.

I am used to biking alone but never hauled 60kg behind me on a slippery road. Here are few things I am interested in: 


Tires on bike and trailer. I have Croozer 2 seater with whatever funky tires it came with. My bike is a folding electric city bike with nice Schwalbe Big Apple 20" tires. 
Mud/dirt. My Croozer came without any fenders. It get's dirty even during summer. 
Kids' clothes. It was 15°C recently and I closed the translucent "window" in the front of the trailer. When I put my hand inside after few minutes of biking it was really nice inside. Boys confirmed but they have a history of lying.
(bonus) Electric 20" wheel in the back. This will be interesting :) 


Updated with bike details. It’s chinesium bike branded EcoBike in Poland. They probably sell under a different brand in other countries.
I strongly suggest you put a studded tyre on the bike (ideally 2, but certainly the back in your case).  I run Schwalbe winters for occasional icy patches (overkill round here, except when they aren't).  This will be important for stopping as well as going. Spinning the back wheel with a trailer is no fun.  The trailer tyres don't matter nearly so much.  They don't really need traction (though side-slipping isn't good). You can get marathon winter tyres in 20&times;1.6" which will fit both your bike and your trailer.

The trailer will get cold inside in sub-zero temperatures.  But it will do a good job of keeping the wind off, so your kids should be fine wrapped up warm.  Makes sure the to start with short journeys, as you won't be able to hear the kids easily (especially if you fit studded tyres) and you want to know before too long if they get cold. I know on a rear seat even above 0&deg;C kids can get quite cold despite gloves and warm clothes, but that's only sheltered by my body.  Some form of hat or even a (thin) balaclava under their helmets would be a good idea.  Lining the seat with a blanket you can tuck round them might also be good if you've got room.

Visibility is important, including visual signs of the width of the trailer. Drivers need all the help they can get to see your trailer in dirty, dark conditions.  Little blinking LEDs as wide as possible on the trailer frame show up well.  I've got 2 of those plus a big steady rear light, as well as extra reflectors and lights on the wheels.  And that's just on the trailer.

Bikes and accessories get dirty in winter.  Mudguards won't help much on somethign so low to the ground, and every trailer is different when it comes to fitting accessories (as I found when fitting parking brakes to mine).  Folding makes accessories really tricky. Overall you'd almost certainly have to make mudguard brackets of some sort, and remove them for folding.  A rear mudguard on the bike would be a very good idea though, and one with a low, soft mudflap on the bottom.