I'm going to try burlap this year, maybe wrapped with rafia ribbon, to make it a little more attractive. I'm not sure about when, though.

This is a really interesting question I think, since my balcony is visible from both the dining room, the street and about fifty apartments.
Last year I used bubble wrap and white plastic. I was told to use white plastic to avoid heating of the pots in early spring. But let's face it, it wasn't exactly easy on the eyes. Burlap would definitely look prettier (even if I splashed a bit of white paint on it) but I've been told that I should avoid natural materials, as they tend to absorb water and thereby loose their insulating ability. Does this go for burlap, or is it just materials like cotton and such one should avoid?

I had read on this website somewhere to use multiple layers of newspaper and cover with plastic bags ( I used the large dark green type) then attached by tying/taping. I am in Z6 and this seems to work. It is work though, esp if you you have multiple pots, but it does seem to protect.

I'm wondering about this too. Maybe bubble wrap around the pot, and a layer or two of burlap around that to conceal it. Artful use of branches, holly, and other wintery plant materials could also help create a pleasing display.