Keeping Aloes outside here in winter is generally fine, but it would depend a bit on where you are at in Phoenix - if you live well within the large urban sprawl area you have very little to worry about. In the last few years it has not really been below freezing in winter at all, we got close a few times. However, if you live more on the outskirts, either at higher elevation or more in the 'real' desert you might still see freezing nights, that is when you want to protect your plants by either bringing them inside or throwing a towel or blanket over them. I have not had to do that in at least 3 years now.
As to bringing your plants inside right now: it is done, so no need to rush it back out, but I would probably have advised against that. Mainly because most Phoenix houses are built to let in very little direct light so in most places you will have trouble providing your plant with bright enough light to thrive (and the windows that do get that direct sunlight, may be too hot to put a plant right behind - though an Aloe may be fine - my SO's house plants do not like the one window we have that catches direct sunlight most of the day - but for the plant jungle that is the rest of our house we have multiple LED grow light bulbs in strategic positions.
So you created a situation were you took it from too much light to what I suspect could be too little light. That is the problem with Aloes here, especially if they are plants that were acquired fairly recently. I have a few in hanging basket that I got on an impulse about a month ago when we were at the Plant Stand of AZ to look at house plants and out of the 4 one and possibly another will not make it, not because of sun exposure but just because of heat. Had I gotten them two months from now they would have been fine and large enough by next summer to not have any issues. I thought about bringing it inside and what not, but decided against it, mainly because while it may save the plant short term, I'd end up with a light (and heat) starved plant that would be difficult - not impossible, but difficult to re-adjust to living outside, because that would be a slow process here, requiring a lot of time in lots of shade, and probably still significant sun burn on the leaves once exposed to sun. And they will likely get some exposure to the sun in summer time even if you keep them on the north side of the house - which is where I grow almost all my potted Aloes. Some get early morning sun, while others get late afternoon sun.
Turns out I have taken very few pictures of my potted Aloes in the last few months (at least the ones in situations that are relevant), but here are a couple of pics with some hanging baskets with Aloes (and a bunch of other plants):
The basket on the right has a clump of Aloe x 'Doran Black' in it, it is in the area that gets the least amount of sun and it is hanging out happy there, but despite the summer heat (which is nothing like last year as you probably know) I water it very sparingly only on cooler nights:
The middle plant is an aloe relative: a large Haworthia that makes the most gigantic flower stalks (it is working on another one right now, but which is not pictured).
Here is a set of hanging baskets from earlier in the summer that is now not hanging there anymore in the same configuration, I moved the baskets with the Aloes that is front and center and the paper spines cactus that is hiding a very small Agave on the left and the pinkish-purple basket that has a Mangave 'Bloodspot' in it to an area with less sun. These are on the corner of my patio cover and would get sun from maybe 1.30-2 PM onwards, that was too much... The basket right behind that has more Agaves of a different type that gets shade a little more by some other baskets that has not moved but that one is now showing some significant stress. The hanging baskets with cacti are still there and are doing just fine with the sun:
There are definitely some Aloes that can be 'trained' to take a lot of sun, but very few are good with all day full sun in summer, most of the Aloes that take the sun in the Phoenix area will take morning sun (I have a few growing in the ground on the east side of my house that show stress, but are growing happily there). The thing is bright outside shade is still a lot brighter than the inside the house lighting of most of the places here in the Phoenix area.
