None of the three options you have described are likely to work out. Probably your best bet is to plant them in the ground and use makeshift protection like hot caps or cloches to keep the shoots from being damaged until the season is far enough along for them to be fully exposed.

What zone are you in? My advice would depend on how quickly your spring will hit. If your ground is workable and your growth doesn't include any buds yet I'd plant them and mulch with something lightweight like pine straw for several weeks. I'd shy away from cloches but that's because of where I live--any left on during a sunny day will cook new growth at my elevation even if the temps were below freezing at night, your area could be completely different. I typically buy a few bareroot peonies every spring and most have growth as you describe, sometimes it makes it through the spring, sometimes the initial sprouts die back with the cold and more emerge as the spring rolls in, sometimes I see no new growth until the following year. The only time I've lost any roots that I planted in the spring was when I potted them and left them outside. I'm in a zone 4b that gets several really late freezes every winter though--others in warmer zones can do the pot thing with just a mulch. If you're in a warm zone you might be able to basically harden them off like you would any new seedling, slowly exposing them to more light over several weeks. You might want to post some pics as well as more details, we'll help out with advice if we can!

Sorry, saw you posted that you're in zone 6 at the start of your comment! I'd still think getting them in the ground as soon as it's workable would be the best option.

Slightly warmer in Zone 7 here at the Jersey Shore, but it may comfort you to know that several of my peonies regularly put up shoots this early - still tightly closed - and we still have the worst of winter ahead this month.

Since yours have been indoors, I think lizbest's advice to harden them off is good advice. Then plant outside and mulch well. Protecting with a cloche (even a 1-gallon jug with bottom cut out) may help during the coldest nights, but be sure to remove it on sunny days lest you "cook" those shoots, as has already been mentioned.

Peonies are surprisingly hardy plants. Once they've had time to become established they should reward you with delightful blooms for years to come.

How is your Peony now？