Does anyone know what happens if potted hardy mums are brought indoors for the winter?

Every year I have followed the rule of waiting until a hard freeze, then mulching our (in the ground) mum plants. But they usually die over the winter. This year we have purchased several very large plants, kept them in pots for the fall, and I would really like to be sure they survive.

What would happen if I just brought them inside? Would I wait till they die down first? Would a cool garage be better? Would I be better off making cuttings now before they die back and trying to propagate new plants?

Any advice is appreciated!