If this hydrangea is a winter-hardy hydrangea (we're assuming yes, as forced florist hydrangeas tend not to be sold this time of year, or in pots that large), then planting it as soon as possible would be our recommendation. Air temperatures are not as important in this situation as they would be with, say, putting a greenhouse-grown tomato or early-sprouted rose shrub in the ground in spring. In fact, root balls kept above-ground (in the pot) all winter run a greater risk of winter injury because they are much less insulated than roots would be in the ground. Container plants also dry out faster than in-ground plants, so must be monitored carefully for watering needs, as getting too dry during winter could doom a plant even if the degree of cold is within its tolerances. Due to the minimal root insulation, even a plant making it through winter unscathed may break dormancy too early since the roots in the pot can warm-up too quickly, and some hydrangea species are notorious for breaking dormancy at the earliest opportunity, often before we are done experiencing overnight frosts that will kill tender foliage. (This can also ruin the year's flower buds, depending on the variety and whether or not it can rebloom later.)

When the soil is workable (not frozen, not too soggy), consider planting as soon as you can. The process is the same as it would be in summer (loosen roots, dig the hole only as deep as the root ball but at least twice as wide), including watering-in the plant well after planting. Mulch will help to moderate soil temperature fluctuations, reduce evaporation, and minimize weed germination.

If you aren't able to plant for some reason before spring (such as the planting site isn't ready, or life gets in the way), then keep the plant chilled (not indoors) and check it for watering needs at least once a week. (Depending on precipitation, temperatures, and wind, it might not need it that often, but best to check. As in summer, feel the soil about an inch or so deep into the pot, and water well once it's become somewhat dry to the touch at that depth. Granted, you have to have the soil not be frozen for this.) The ideal way to overwinter potted shrubs and trees is to heel them in. This is just like planting the plant with the pot left on, so it receives the benefit of in-ground insulation (though the potting mix might still dry out faster than the soil surrounding it, which makes watering without creating a bathtub around the roots harder to do) while being able to be moved to a new location, or planted properly, in spring. Nurseries overwintering cold-hardy inventory tend to either heel plants into beds for winter, build a berm of soil or wood chip mulch and use that to heel plants in above-grade, or keep the pots in a barely-heated greenhouse that lets them get the chilling they need while shielding them from drastic temperatures; it also helps with watering if the hoses aren't frozen. An alternative for the home gardener without such a setup or the ability to heel it in would be an unheated shed or garage as a cold storage place, as long as you can periodically check the plant for water. As temperatures moderate (usually!) in late winter or early spring, the plant can be brought out onto a porch, deck, or somewhere in the yard, assuming deer won't find it as it leafs-out.

Since the hydrangea is dormant, the amount of sunlight exposure this time of year isn't too important, but eventually its final planting location will depend on what hydrangea variety you have and what its light preferences are. Most can handle full summer sun, but some prefer a mix of sun and shade to grow well and look their best. If the plant tag didn't identify the species/variety, we can probably determine what species it is from a photo of the dormant plant.

Miri