My guess is that in a Z7 they will be fine, I would be comfortable planting them out in my cool coastal Z8, and you must have at least another 2 months before frosts? The roots will continue to grow if the ground isn't frozen, frost will nip back the tops but leave the roots establishing. They may have an extra hurdle getting established with the peat pots though, not my choice for seedlings. You may want to take a box opener or knife and make a slit down the sides in a couple of places just to be sure those roots are establishing into the soil outside the pots without any resistance.

In zone 7 you may be okay to plant them out. How big are the seedlings? I've got 2-3 month old Echinacea seedlings I started in May that are ready to plant out, they are 3-4 inch clumps now. But it's been so dry and warm, and they are easier to water in the containers, so I haven't planted them out yet. Really waiting for a good rain, the ground is dry as dust!

If your seedlings are tiny and you have doubts, you can overwinter the plants in the pots in the garage or basement, and water about once a month to keep roots moist. I over winter some tender perennials (like Salvia guaranitica) and sometimes small seedlings every year in the garage with pretty good success. Just have to remember to water them once a month or so to keep the potting mix moist.

I am going to plant some seeds as well tomorrow. Purple basic coneflowers (cheap seeds!) I cut the bottoms out of some cheap plastic pots and stuck them in the ground, so I can easily remove later. I mostly did that so that I remember where I planted them :) I figure this is the time of year the plant would naturally drop seeds so worth a shot.