Can you send pictures of the chicks? If they have feathers, the colder temperatures shouldn't be as much of an issue, but if they don't have enough feathers, then they can't regulate their body temperature enough to stay warm.
It is smart to keep the younger ones separate from the older ones, but if you have the space, one thing you could do to get them used to each other is move the older chicks to a dog crate, but keep it next to the younger ones' bin. That way, they will hear each other and maybe see each other, which will make introducing them as they get older much easier. Then, you could either keep the older chicks there or move them to your garage when the weather warms up. Then the rest of your plan sounds good, but you want to make sure that there is room in your coop for the dog crate where it won't be under the perches, so the smaller ones won't get pooped on at night.
A tip for introducing the chicks into the coop is to keep them in just the coop part for a couple days, then let them out into your run or yard, whichever you choose to do.
It's fine to play with them inside, as long as you keep them in a safe area. (For example, away from unfriendly animals or high places where they might fall.) The only downside is that they are likely to make a mess wherever they go.

We had ours the laundry room part of our basement, with a baby gate set up so that my dog couldn't get in. There, I would just take out a couple at a time to let them practice flying short distances, such as from my knees to my hand. They can get pretty high! When we had chicken wire over the bin that we kept them in, if we took it off they would fly up and out of the bin to sit on me!

In the dog crate, you can put long sticks across the inside so that they are supported by the horizontal bars of the crate, at varying heights to let them practice perching. Taking them out inside is a great way to get them used to different temperatures, socialize them to you, and just have fun watching them! I hope this helps, and feel free to ask anything else.
Have fun with your flock! Looking forward to hearing how it works,
-M