Yes, you can dig them up, put them in a pot, find a spot in the house where it is bright but not too hot keep them watered and they will bloom, OR you can take cuttings, root in water and start new plants that you can nurture during the winter then plant outside. You CAN't dry like geraniums though, when dry, this plant is dead. You can actually have flowers indoors all winter from bringing Impatiens indoors.
Pauline

Re cuttings in water: How long should a cutting be? Do I strip off most of the leaves? Normally, how long does it take to see roots? Thanks for the advice.

I would like to consider this topic myself. However, when removing from soil, is it necessary to remove the entire root system? Some of these roots are really imbedded in the ground. I would imagine leaving the roots might chance some disease???? Please advise

I overwinter geraniums by drying and pottting after they go dormant. I do someting similar with impatiens. After the first frost, but before the ground freezes, I dig up impatiens roots. I then shake off the soil and plant inside under fluorescent lights. As the new growth develops, I pick off dead parts from the previous growth to prevent mold. This has worked well for me. (Seedlings will also grow and I pot these as well.)