When i had potted figs, i kept them in an unheated shed with no problems. About the same temps as you get.

Anything above 42* = weak, etiolated growth. I would opt for the barn, but cover the trees with an overturned cardboard box. This will trap the geothermal heat coming through the floor & your trees will be fine. Remember to toss a little snow on them from time top time to keep the soil from drying completely. Ideal overwintering temps are >32* but Al

I would not worry about covering them. My shed was free standing, uninsulated and open to the elements underneath.

" I would not worry about covering them " may be true for Zone 7 but Bart is close to Zone 6 so he may need some caution. I am zone 5 and some of my plants in unheated garage last winter had to wait until late June to green up. That may be because the feeder roots and the next thicker ones were dead and these plants had to regenerate some new roots before greening up.

I get single digit temps, 0-5 degrees, same as OP.

Bart:

Do a quick search within this forum for all the answers to your overwintering questions. There's plenty to read.

Short, and sweet, ..... since 2007, I have stored my containerized fig trees in an unheated, garden storage shed. I have read that temp's inside the shed are about 10 degrees warmer than outside temps. I throw a few shovels of snow into the 20-gallon pots for watering throughout winter months. The trees go in around Christmas, and come out by the first weeks in April, or when buds start swelling. Temps. here in the Bronx, NYC rarely go below 10-15 degrees, even at night, and the fig trees have come through the winter with few, if any problems. Try to prevent the root-ball from freezing solid. Read the inverted cardboard-box suggestion again.

You'll do just fine. Happy growing.

Frank from Da-Bronx

Thanks folks!!! The shed it is! Now who wants to help me clean out a spot?!?!?

Thanks again,
Bart

I have never over wintered anything in zone5b-6a, but tapla seems to have the right ideal.
He know a great deal about container plants.
I too have 3 fig tree for the first year & am going to put them in the basement, when temperate gets below 20 degrees.