This is what I think would happen. The inside of the shed would be warmer than the outside. The perennials would start into growth early. There is no light in the shed, so the new growth will be sickly and weak. This would vary from one kind of plant to the next. Also, the potting mix is very likely to dry out over the winter. I know from experience that this will weaken or kill some plants.

There is also the problem of extreme cold weather. Plants in pots are very vulnerable, because the roots get just as cold as the above-ground parts. Maybe you should plunge the pots into bark, and cover them with an insulating material, like old carpet or bubble wrap. If you are going to do all that, it might be better to store the plants outdoors.

You may also have to protect against mice.

Daylilies are perfectly fine in pots over winter outside in the rain with no protection unless your location gets a lot colder than Portland?

I had more than a dozen potted daylilies (gallon plastic pots and bigger) the last three winters.

I pot up any daylily purchased out of bloom until it blooms before planting out in my garden.

I do this every year with my geraniums and fuchsias. This past year the geraniums did not make it at all but we took them in later than usual (Thanksgiving).