If you live in Brooklyn, you probably have a yard which is surrounded by other houses, perhaps a fence too. So, you will probably not have too much wind to cope with. Since it's not too wide, you will probably only get to it from the wide sides, not the ends, makes a difference with your covering.
If I had your conditions, based on the odd size overwintering house, and in your specific location I would:
Construct hoop house
Cover first with burlap, securing the far side tightly to the ground, perhaps burying it a couple of inches, then stake it to the ground
Cover the burlap with a tarp loosely, perhaps the blue kind sold in hardware stores, NOT poly which will hold heat
Perhaps only cover with blue tarp when high winds are expected or if the temperature forecast is below 20F
Leave the ends open
Secure the wide part with stakes, allowing for easy inspection
In late winter, remove the blue tarp, leaving the burlap
That's what I would do.
Good luck!
Bill