How cold is too cold for 10 week old chicks? It depends on how your coop is built, ventilation and draft protection, and a bit on how they have been acclimatized but well below freezing.
I’ve put 5 week old chicks that were raised in a brooder in the coop out on weather like yours. The brooder in the coop was fairly large, had good draft protection, had good ventilation so it could cool down, and I heated only one area, letting the far reaches cool off as it would so they could get used to cold weather. When they were 5 weeks old I moved them to an unheated grow-out coop that also had good draft protection and good ventilation. When they were about 5-1/2 weeks old the overnight low got to the mid 20’s Fahrenheit. They were fine.
I usually let my 8 week olds range with my adult flock, but they have a whole lot of room. Your space looks a little tight for integration with that many. Chickens can normally live together quite peacefully as a flock once the pecking order is set and they are used to each other, but it can sometimes get violent setting up the pecking order. One way the chickens have learned to cope is that when there is a confrontation, the weaker runs away from the stronger. Immature chicks are going to be weaker than mature chickens so once they figure things out, yours will want to avoid the older to start with. They need room to avoid and run away.
Housing then together where they can see each other but not get at each other is a great idea. It does help cut down on potential conflict, but it does not eliminate it entirely.
I’m not saying you can’t do what you are talking about. It’s very possible you will be very successful. I suggest you provide separate feeding and watering areas so the younger ones can eat and drink without challenging the older birds. Also provide places they can hide under or behind to avoid the older birds.
I find that a lot of violence takes place on my roosts. Your young ones may not be roosting yet, but I’ve found it beneficial when integrating younger birds to provide extra roosts, a bit lower and away from the main roosts to give them a safe place to get away from the bullies on the roosts.
Something else I normally do when integrating younger birds is to open up the coop at the break of day to give the younger ones more room to get away from the older. It depends on how this goes, but I usually do this for about a week.
The tighter the space and the younger the chicks the more risk there is involved. What you are talking about can be done but with your space there is some risk involved. Just watch them carefully for a while and good luck with it.