Hello there I have almost 9 week old Easter Egger checks that have been in my garage in a brooder.
How cold does it get in that garage? I don't know if you open and close that garage door but there is a good chance they have not needed that heat lamp for a few weeks even if you do open that door. If it gets cold enough that would be a good way to acclimate them.
At nine weeks they should survive even those low temperatures, provided their coop or brooder has decent ventilation but they are also protected against a direct breeze hitting them. They will be more comfortable if they are acclimated but they are as feathered out as your adults. I don't know what you do special for your adults in those temperatures. Even when it gets below 0 F I do nothing for mine except give them the chance to stay in out if they want to.
I also have an existing flock of buff Orpington‘s and wondering when I can introduce my new flock to the old flock and also considering these temperatures I feel a little lost.
I don't know what your facilities look like, that can make a difference. How much room do you have in the coop, how much room in the run, and when is any run room available? You only have 4 adults which often means space is pretty tight. My brooder is in the coop so the chicks grow up with the flock. So my integration starts when they go in the brooder after hatch and I usually have them roaming around by five weeks. But I have a lot of room inside and outside and that outside room is available pretty much any time they are awake. I don't think you have that.
Without knowing what your facilities look like and what you have to work with it's hard to come up with any specific recommendations but some generic things we do is to house them across wire for a while to get them used to each other, give them as much room as you can, maybe improve the quality of what room you have by adding clutter (things for them to hide under, behind, or get over), and provide widely separated feeding and watering stations hopefully out of line of sight. If there is enough size differences in the ages you may be able to use the safe haven/panic room concept where you have openings that the chicks can get through but the adults cannot so the chicks can mingle as they want or stay safe.
You can start this process as soon as you wish. Build a pen that the adults can't get into and put the chicks in there. I don't know when you can start letting them mingle, that depends on a few different things. It will be probably harder to integrate in the winter, not because the chickens are cold but because they may not have access to the outside room because of wind or snow.