You don't mention where the peony originated - hopefully somewhere in the state or a nearby state so the plant is acclimated to the upper Midwest growing conditions.

The soil in the pot will freeze solid in the winter, so unfortunately leaving it in the pot on your patio or deck is not a good option. It's best to plant it in your garden and the sooner the better as the weather is changing. I recommend asking your association for permission to plant it. It is not an invasive or aggressive plant nor is it a very large plant. It also has sentimental value to you.

This is not the best recommendation and I admit I have never tried this myself: if the association does not allow you to plant the peony, you could try to overwinter the root.

Place it in damp peat moss (damp like a rung-out sponge) in a ziploc plastic bag in the refrigerator. Dust it with a fungicide for protecting bulbs (check at your local garden center).

Check it every few weeks for rot or mold. Clean off mold with a soft brush or towel. Prune off any rot with a sharp knife.

In April or early May, plant the peony root 1.5" – 2” deep in fresh potting soil and in a large clean container. Place it in a warm sunny window and water. Keep the soil moist (again, not wet).

When daytime temperatures are 50-55 degrees, acclimate the plant to the outdoors by moving the peony in the pot out to a protected location during the day for a few hours. Bring it indoors at night. Increase the amount of time outside each day over a couple of weeks until finally you can leave it out for the summer. Hopefully, it will bloom for you.

Hopefully, the association will allow you to plant the peony. For information on planting this hardy perennial: http://www.extension.umn.edu/garden/yard-garden/flowers/planting-peonies/

Note you should plant peonies roots about 1.5" – 2” deep - any deeper and they may not bloom well. Plant in full sun in well-drained soil with plenty of room for the plant to grow to its full size. Install a peony cage at planting to support the plant as it grows. A peony cage is similar to a tomato cage except broader in diameter and not as tall. After blooming, cut off the dead flowers before they form seed heads.

Note that there are some peony diseases like powdery mildew. Diseases can be managed by spacing plants according to their mature size to allow for air circulation, and watering at the base of the plant. Do not use overhead sprinklers as this practice can increase the likelihood of foliar (leaf) diseases. Mulch the base of your peony with about 2" of wood mulch to converse soil moisture, suppress weeds, and reduce splashing of soil onto the lower leaves. Mulch also creates a very nice finished look to your garden beds.

Here are a couple of publications to help you manage these should they occur:
http://www.extension.umn.edu/garden/yard-garden/flowers/powdery-mildew-on-ornamental-plants/
http://www.extension.umn.edu/garden/yard-garden/flowers/diseases-of-peony/

Feel free to reply with additional questions.