Overwintering Strawberries under lights

Last Spring my neighbor gave me a small little strawberry plant that has since propagated into about 10 different containers. I read that strawberries don't produce the first year so they just grew and grew and I let them propagate all summer. Now that winter is upon us, I have to decide what to do with them. Under normal circumstances strawberries must go dormant in the ground over winter like any perennial. Over wintering outside here in Zone 5 Chicago in pots kills a lot of tender perennials so I'm a bit wary about leaving them outside. I had considered bagging the pots and putting them in a dark, but not so cold, garage for the winter. I also have two indoor light setups, one HPS for flowering plants and one fluorescent setup for vegetative growth plants. I'd like to overwinter the strawberries under the fluorescent lights over the winter but am a little unsure as to how this will screw up their internal clocks since my lights are timed to give 10 hours of light per day. Does anyone know what kind of problem I'll have with strawberries being over wintered like this? I don't have the option of putting them in the ground because I don't have any yard.
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I would put them in the garage. I shop at a nursery that sells bare root strawberries that are kept in a humidity controlled, refrigerated room. I believe the temperature is around 40F. If that is about where your garage is, they should be fine.
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Is there some reason you can't plant them in the ground?
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