The vast majority of Cotoneaster species are extremely cold hardy. I would not forgo a natural dormancy period - that is never advised for the long term health of a typically hardy woody shrub or tree - and put it outside. Zone 8 is not too cold for this plant at all and the only concern I would have is the soil in the pot freezing if you did perhaps experience an extended cold period (down into the low 20'sF or less than -4C). And that could cause root damage - there will be no adverse effect to the top growth.

Is there somewhere outside where you can sink the pot in the ground? That would be ideal. Otherwise just put it outside somewhere where it is semi-protected and only bring into your cold storage place if severe winter weather threatens

Thanks for your help, gardengal48!

I live on the second floor of an apartment building, so no ground to place the pot in. My apartment has an inset balcony, so there's enough shelter from the elements and sun during a large part of the day.

For extra measure I'll put the pot in a bigger pot and fill it with bark fines for insulation.