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Sorry for your loss!
Since your basement is cold then they will have an easier time getting used to the cold outside. But if they are only 2 months old then you should wait a little longer especially if it's in the single digits. You can probably let them live outside once they are around 3 months. (A little before then is fine.) Normally, you could let them out now but since it's so cold, you should wait.
Once they do go outside, their coop should have all the necessities needed for surviving in the cold. The most important necessities include ventilation, dry bedding, heated water and 4" roosts.
You need good venting in your coop ceiling to rid the coop air of all this unwanted, moist air. If you don't put in good ventilation, during those really cold winter nights, all this moisture is going to rise up to the ceiling since warm air rises, and if it has no place to go, it will fall back down as water or frost making your birds very cold and uncomfortable.
The ideal way to create good venting is put in 1 square foot per bird of venting in the roof. Split it half and half on either side of the ceiling, one vent higher than the other. If the coop ceiling is not very high then position the roosts lower to the ground. You don't want any venting near the floor. This will create drafts. So what really does this do? It makes it so the moist air from the chickens slowly rises into this positive air coming in the lower vent and out the upper vent. Birds themselves put out heat. So they literally are roosting in a nice warm bubble of air. The moist air rises and goes out these vents. You don't want to disturb this air space around the birds with drafts. So make sure to seal up all cracks above the birds a foot or two.
Venting can be worked on those cold winter nights by closing off some of the lower vents to slow air movement in the coop. You never want to close off the higher vents. You will not retain much heat by closing off the vents, but you will keep the birds drier, especially if it is a bitterly cold night and you use heat lamps. Hot air meeting cold air creates condensation, so keep the air moving to prevent this.
~Thanks to Two Crows for the info.
Other things to do to help keep your chickens snug this winter include using straw as a bedding, using the 4" inch side of a 2x4 roosts. I also put a towel that has been in the dryer and put it on the roosts to warm their feet. Make sure that there is no water spillage or moisture collection on the bedding as this can also result in frostbite. On the very cold nights you should rub vaseline on the chickens' combs and wattles to help prevent freezing.
Here's a link on frostbite and ventilation.
https://www.backyardchickens.com/a/frostbite
https://www.backyardchickens.com/a/chicken-coop-ventilation-go-out-there-and-cut-more-holes-in-your-coop
You don't need a heat lamp if you have ventilation, proper bedding, proper roosts and proper feed. In the winter you should be feeding your normal layer, grower or chick feed along with scratch as this will keep the birds warm especially if you feed it in the evenings.
Bedding that is warm and absorbent is also necessary. Wet bedding mixed with the cold temps and wind chills equals bad frostbite. So either use straw, shavings or shredded paper. Straw is possibly the best bedding to use in winter. Line the nests with straw to help prevent eggs from freezing. Bales of straw help act as insulation and keep the coop even warmer.
Heated water bowls are also imperative. Chickens drink non-stop in winter and they can't do that if their water is frozen! So either buy a heated bowl or use a heated base on the bottom of their regular waterer. I've also heard of people who place a 40 watt bulb in between bricks and then put the water on top in a bowl. Make sure the waterer isn't plastic.
Here is a link on things to and not to do in winter
https://www.backyardchickens.com/a/things-to-and-not-to-do-during-winter
Good luck!!