I disagree a little. I think you're heading towards the time when they might start to rebel, but really, I think if they sense fear or hesitation from you they might not jump on board. I would ask the older kids to help me downsize their things - but don't take no for an answer, either. You ARE the mother, after all, and you need to lead them, not the other way around. (I didn't say boss them around or bully them... just lead them!)
I agree with starting small, but perhaps make it a routine that every Saturday morning you will take a trip to the thrift store where you will ALL get rid of some things. In 3200 square feet I'm sure even they will find things they no longer need or want. Have some of your stuff and some of their stuff. And get rid of all trash, simplify your routine (fall is a good time to do this...). Even down to something like what's in the kitchen and pantry, what you buy at the store, what laundry products you have. Give stuff away. Instead of having whatever processed food at home, look through your food stores and see what you can freecycle, or just eat what you have and don't buy any more. Make a meal plan so they know what to expect, and then have one or two healthy snack choices available. That's it. You are the mother. You are still in control. They're not even teens yet. Take control of the home and little by little pare away not only YOUR stuff... but yes, you can have them pare down their stuff. Not all at once, but make a goal of, say, the next school year.
Incidentally, it's great you're starting BEFORE the holiday season. Get your family on board NOW, so they're not disappointed when December rolls around and they have fewer presents than in years past, maybe. Focus on doing stuff together. Even if they're supercool tweens, I'm sure on some level they will appreciate the parental involvement, and it will make up for the stuff. Which... I promise, if you take it little at a time, they won't even notice before long. They'll discover cool things they forgot they had.
Or heck, if you need to, bribe them - for every box they fill up to donate (to those lesser fortunate or whatever - get them to want to give the stuff away! tween is a great time for compassion stuff) or throw out in the garbage, give them a small monetary amount to use to, say, redecorate their rooms in "big kid" style. (If you usually spend a lot of money anyway on them, it probably won't be more than you're used to spending.) If you feel like it and they will buy it, for things that they're not absolutely in love with but want to hang on to, convince them (nicely) that that's for younger kids and they're ready for xyz now. I mean, dont' shame them or anything... but think of what would motivate a tween, and go with that.
BTW we lead a pretty simple lifestyle but LOVE Disney World. We just got back from our trip as well... thankfully we tamed the souvenir monster and didn't have too much to bring back home with us. Don't feel bad and feel like you need to cut it all out. Disney week is our yearly time to go all out. Junk food, TV, the whole lot - but then we leave the chaos and excess there!! And we come home to our more simple lives. It works for us. :)