I think it depends on the kids. I have five and some of them are runners and active, and others will sit quietly and play (making up imaginary games). I have two readers who will curl up with books but the others won't unless it's bed time.
I have one son who I have to send outside when he gets like that. I say "time for outside!" and then they all mostly get their snow gear on and follow him out. We also changed our garage into play zone during the winter (hockey net, scooters etc.) so I send them down there if the weather is bad. My sister used to set up a sand box in the winter in her garage, and cranked the heat and let them play in it during the winter.
Hulla hoops in your basement, lots you can do to get rid of that extra energy. Definitely outside every day. I pick up new gear (nothing expensive) just to change it up - so a new soccer ball, a new kite, bubbles, whatever the season. We set up a rink in our back yard in the winter. That has saved my sanity.
As for sitting down and playing with toys, mine don't do a lot of that either because they have siblings (my younger kids did it more when the older ones were at school). When all home, I think they look for games to do together. My kids will all pick up their Nerf guns (we just have a big pile of them) and chase each other.
When I want them to do quiet time - here's what I do. I have sets of things that all ages can enjoy - even the big ones.
I will set up this big race track we've had for years - just set it up in the play room. Or a big old train set (even though some of long outgrown). Or I will get a big puzzle they would like. Or I'll sit down and start up a game they can all join in. I'll make a big batch of play dough. Then I quietly back out of the room without them noticing.
Will your kids play Lego? We have a big spot where they can just dump it and leave it out for a few days. ALL my kids will get into that. I will give them a challenge if they are stumped - who builds biggest tower ...
My girls have Barbie and doll houses and no, they don't usually play with them as much as I had thought. If I pull it out in our sun room, and set it up for them and just start them off, they will join in and sometimes that will keep them happy for hours. I let them leave it up for a few days. If their friends come by, they join in.
Do you swap your toys out and put them away? That was the best advice I ever got. I keep everything away unless they pull it out to play. So we have a big box of costumes that I keep hidden away. On rainy day, we'll go get it. I sometimes have to join in to get them going, but after a while imaginations take over. They'll do a parade around the house. Or I'll pull out our little drum, harmonica and stuff - and they will combine a band with dress up. Even my older ones will do this just for a laugh.
I think unless I started them off, they wouldn't necessary think of these ideas themselves. Some of my kids mind you are just happy to sit and play quietly with their Little Ponies, or do hockey cards. I think a lot of it depends on their personalities.