Personally I would prioritize healing over reintegration if you are able to handle a house chicken until you get a break in temperatures to start trying ot reintegrate. After 3 weeks she'll be going in at the bottom of the pecking order and if she's not back to 100% she may get beat up depending on the temperment of your other birds.
You are also right to be cautious about the temperature disrepancy after a long indoor stay. Integration issues aside, it is possible for an adult chicken's metabolism to basically un-winterize due to a lengthy indoor stay, resulting in a bird that looks like it should be fine in freezing temperatures but is actually significantly more prone to hypothermia and frostbite. Birds that have had major physical stress of some kind will also be less able to handle cold. I have two such birds right now. They have issues shivering starting in the 20s right now while my other birds act like 0F is just a minor annoyance. There are degrees of shivering to watch out for as you re-aclimate a bird to colder temperatures. If it just feels like a cat purring when you place a hand on the chicken's back, it's probably ok. If the whole bird is shuddering, that's a hypothermia risk.
The way I'm trying to re-winterize my two house birds is through daytime exposure to not-too-bad but still colder temps when I get them. They are used to roughly the same indoor temps as yours and started getting some outdoor time when I had a couple lucky days with a highs in the 40sF, and rapidly(within 5 days-ish) were ok down to about 28F. However, they still struggle with 20sF. Although they'll be indoors on awful days coming up soon where it's something like a high of 15F and a low of 9F, after that I will be trying to use a brooder plate that can also be used as a coop heater in their enclosure to give them a way to warm up when needed and be away from it when they can tolerate the cooler temps. I used that method once before when I had late-in-the-year chicks that weren't quite ready for a nasty winter and it worked really well. If you can set up something like that for your girl once she's healed, that would be one way to get her reintegrating - but wind protection is essential, so you ight need all sides tarped to a degree rather than just two.
You are also right to be cautious about the temperature disrepancy after a long indoor stay. Integration issues aside, it is possible for an adult chicken's metabolism to basically un-winterize due to a lengthy indoor stay, resulting in a bird that looks like it should be fine in freezing temperatures but is actually significantly more prone to hypothermia and frostbite. Birds that have had major physical stress of some kind will also be less able to handle cold. I have two such birds right now. They have issues shivering starting in the 20s right now while my other birds act like 0F is just a minor annoyance. There are degrees of shivering to watch out for as you re-aclimate a bird to colder temperatures. If it just feels like a cat purring when you place a hand on the chicken's back, it's probably ok. If the whole bird is shuddering, that's a hypothermia risk.
The way I'm trying to re-winterize my two house birds is through daytime exposure to not-too-bad but still colder temps when I get them. They are used to roughly the same indoor temps as yours and started getting some outdoor time when I had a couple lucky days with a highs in the 40sF, and rapidly(within 5 days-ish) were ok down to about 28F. However, they still struggle with 20sF. Although they'll be indoors on awful days coming up soon where it's something like a high of 15F and a low of 9F, after that I will be trying to use a brooder plate that can also be used as a coop heater in their enclosure to give them a way to warm up when needed and be away from it when they can tolerate the cooler temps. I used that method once before when I had late-in-the-year chicks that weren't quite ready for a nasty winter and it worked really well. If you can set up something like that for your girl once she's healed, that would be one way to get her reintegrating - but wind protection is essential, so you ight need all sides tarped to a degree rather than just two.
