I do it at the end of winter after all chance of frost has passed. It's not that they freeze readily but that I like them to have as little stress as possible. But I wouldn't hold one over in a store pot just to wait for spring. We hardly have any winter anyway. Of course, most store plants become available in early spring. But I know there are valid arguments for winter planting, mainly to get more roots established before heavy leaf load appears in spring. I think pretty much any time, other than in full sun in Texas August, so long as you watch and think and deal with situations that might arise, most of which can be approached logically.
And since you want containers, you're free to move them in or cover them in a deep freeze, which you might want to do anyway with containers. I think containers are very different in their demands on the gardener than in-ground. In dry weather, it is hard to keep them evenly watered. Container dry so quickly and have no other source. And with the water being contained, it's easy to overwater. Not really overwater so much, but stay over-wet longer than in-ground. And there's no giant Earth heat sink in hot summer or heat reserve in winter. You have to do more thinking for the plant.
I'm liking more and more the unglazed terra cotta watering spikes that screw onto the end of a drink bottle. Like a Forsyth pot, they let the soil take what it needs. without being an uncontrolled drip. If they aren't sufficiently attractive, they can just be used in the hottest months when the plant needs all the help it can get. Search WATERING SPIKES on Amazon.
There's also a pricey but interesting thing from Oyas Irrigation (see Etsy) and a much less expensive one from GrowOya which should work as well. There essentially a gourd shaped clay thing with a neck wide enough to fill easily. You bury them in the soil near your plants and keep them filled. The plants will send roots their direction, just as they would with any water source, and will take water from the soil around the gourd, which sets up the osmotic pressure that draws more water from the gourd until balance is restored. It can't over water or underwater because the plant is in control.
They are exactly Forsyth pot components, but there's no open pot on the surface. You can do a classic Forsyth arrangement, if you have room in the container for the clay pot. I like the "oya" stuff, because unless the clay pot in a Forsyth pot is quite large in relation to the container, it needs to be filled more often. And in a Forsyth pot, as Forsyth himself advised but many people forget, the plant (really cuttings more often) should be against the underground portion of the pot. It also let you lift the pot out and see if cuttings are rooting.
With the olla type waterers, you can plant closer to the narrow neck, and the plant roots will naturally be close to the water source. Of course, with the "oyas" you can't see the water level, so you have to learn how often to top it off. But they're more usable for in-ground, because you don't have that big open pot catching debris. But you could also work out some covers for the clay pots in classic Forsyth pots and probably save some money, since six-inch clay pots are about $5 a piece new.
I spent a lot of time on that because I don't think high air temperature itself does things like roses any harm, but it does dry out a container badly, and those things above can fix that. I could certainly see a line of roses in a long rectangular planter with clay pots of oyas set between them. I have some approximately 24"x8" containers with peppers in one and mint in another, and I'm dropping a 6" clay pot in the middle of each between the plants.
You can find information on the Forsyth pot on the Internet, although it will be misspelled "Forsythe." It's really just a clay flower pot with the drain hole sealed with a cork, silicone, clay, etc., and stuck into the soil to the level of the rim and kept full of water.