As long as the bulbs are hardy for your area, most will be just fine outdoors in a container. They can freeze solid. The squirrels dig mine and replant them just below the soil surface, so I know they have to freeze. One set of tulips is exceptionally noteworthy: squirrels replanted 'Miranda' tulips just below the soil surface and they've been blooming wonderfully and increasing very well in the several years since.
Make certain that the soil in the container has good drainage so that they don't rot.
Also, I'd be cautious about storing in an area where they might get too dry. I think the only potted bulbs I've lost were forgotten in a *safe* place and dried out after they started growing.
What type of container were you planning on using? Grow pots, or something else?
