Can you sink the pot into a larger container of mulch (and put about 1" or so of mulch on the surface too)? Then keep it in the shed.

In case you don't know, don't water it once the soil freezes, not until it's thawed enough (in spring) to dry out enough to need some.

I bring my cotoneasters in during the coldest parts of the winter and they are very happy. They're just gone out on their holidays now.

In most cases cotoneaster is so vigorous it needs repotting every year anyway, so you could simply lift the plant from the pot, then plant the root mass and mulch well. Lift and repot in the spring. I usually overwinter my plants in an attached unheated garage. The only issue associated with that practice I see as a negative is that the plants usually leaf out 2-3 weeks before their counterparts in the landscape do, which means you'll need to move outdoors and back under cover as temperatures dictate until it warms up enough that it's safe to leave them out w/o concern for chill injury.

I toss a little snow on them from time to time over the winter, and I'd do the same if they were in the ground - or water them - especially if there is no snow cover. You really do need to be sure that if you bury the pots in the ground that you are attentive enough that the root mass doesn't dry out in the pot, which can happen very easily when all the roots are contained in such a small volume of soil.

Al