It's hard to understand what you've writtten, but I gather you can either store the trailer in the basement or upstairs on your apartment balcony, is that right?

Presuming it is, I'll first say that your trailer will be less affected by cold than the bike, so storing it outside isn't a big deal, although you should keep it covered to prevent snow, sleet, and wind from really freezing it up.

Ideally, you'd want both the bike and the trailer inside so that they could melt off accumulated slush and warm the lubrication for better running. It's also much nicer to handle and connect up hitches and buckle in kids when everything isnt stiff and cold.

The big issue for you is convenience. You'd have to go up, drop the kid, go down and unhook the rig, take the bike back up, go down, fold the trailer, and then carry it down to the basement. Reverse that in the mornings...I get it's a PITA. I suppose the only alternative would be to leave the trailer outside the apartment building; if you could secure it and tarp it, that might not be so bad, but is it any easier than folding it and putting it downstairs? Probably not.

Is there a carport you could lock the trailer under?