I actually had to mapquest to see how far we generally drive on our "big" ski vacation. We've gone as far as 400+ miles to Tremblant, 300+ to Smuggler's Notch and Bretton Woods, and probably the shortest distance was to Okemo last year which is 215 miles.
So, yes, with a family of 5, we drive 250 miles regularly for a ski vacation. We won't really do it for less than 4 ski days. When we plan a vacation, we look for a mountain within 5-7 hours of driving time (as predicted by mapquest) that's large enough to keep us busy but not bored for 4 days of skiing. It definitely means extra vacation time to get there. We need a 5-6 day window for 4 days of skiing. We used to have the entire Presidents Day week off, so the kids didn't have to miss school. Lately though, we've only had a 4 day long weekend, which just isn't long enough in our opinion. Some of that is because of the cost... with a family of 5 it just doesn't seem worth it to drive that far and pay that much to ski on the most crowded weekend of the year for 2-1/2 days on the snow... We've tried to leave after school so the kids miss one less day and so DH can schedule conference calls later in the day and NOT take a vacation day - and we've also left by noon on our last ski day to get home. That actually is pretty standard for us since our kids feel like they've skied most of the mountain that they are interested in by our 4th ski day. Even on skis they get bored easily so if they've skied most of the runs and gone back to their favorites a couple of times, they're ready to leave.
Anyway, other than taking snacks for the car and 2 boot dryers (family of 5, LOL), I don't think we pack anything different than we would if we flew somewhere. If we did fly somewhere, we'd all take boot bags full of clothes, helmets, ski boots etc - and we might (or might not) take the sport tube with my skis and DH's. But I think we'd rent equipment for the kids. Whether we fly or drive, the kids are responsible for their own entertainment. Between iPhones, nintendos, and e-readers, they don't need much room to bring along whatever they need. When we do drive, we bring along movies for the car. The kids choose the movies, and DH and I might add a couple - but only if we know that our accommodations will have a DVD player. Our kids are ages 10-15, but when they were younger, we took along a few extra bags with things like coloring books and maybe a new power ranger or whatever as a treat. I will say it's harder to pack light when you have room in the car or in a carrier on the roof of the car...
When we lived in Delaware and Maryland, we took vacations at Sugarbush. We would leave on Saturday, drive to Southern Vermont where we spent the night with friends. We'd have a nice visit and relaxed morning at their house and leave around noon. We'd stop at a grocery store in their town and get food for the week... and since it was generally plenty cold, we'd throw the food up top in the carrier where it would stay cold. We'd get to the mountain mid/late afternoon on Sunday and ski Monday - Friday. Then we'd either reverse the process or, once or twice we left about noon and drove straight through, hoping our kids (toddlers and babies at the time) would sleep - which they didn't! But we'd be home with at least one more weekend day before we had to face the week ahead. Pulling kids out of preschool for an entire week was a "no-brainer," and it gave us both weekends for travel flexibility. Trying to minimize the time we take kids out of school is definitely more challenging and adds some stress to the process. But our schools give each student laptops and much of their work is done/turned in online - so driving would mean they could keep up with their homework more easily. I'm not sure I'd want to risk taking the school laptops on a plane...
Would I drive that far for a weekend of skiing? Probably not... We'd hit southern VT which is more like 175-200 miles. I can't see taking two days off to drive somewhere to ski 2 days. I want my ski days to outnumber my driving days, LOL. Also, 250 miles takes us to large enough mountains I think we'd want more than 2 days to explore...
As I write this I'm debating where to book our annual vacation... it's either driving to Tremblant (a second visit for us which would be a first) or actually getting on a plane and heading west. And as usual, one fo the driving factors will be deciding whether/how long we can afford to pull the kids from school for the travel.