First of all, 4 1/2 is certainly not too young to start skiing. Many resorts have classes (NOT daycare) starting at 2 - 2 1/2. (The only thing I don't like about those kiddie classes is when they snake their way past me on the slopes!)
We have skied some of your choices, and IMHO, some are great for kids and beginners and others are not. The ones we've skied are Vail, Aspen, and Snowmass. We've also done Breckenridge, which we loved, but is not on your list.
Breckenridge is our favorite, for several reasons. The resort is very skiable, with all sorts of terrain and wonderful facilities. But the best thing about Breck, to us at least, is the town itself. It's a real place, with real people -- not like the pretentiousness of Vail. The only negative about Breck is the altitude. The base there is 9,600 feet vs. 8,100 feet at Snowmass. That difference gives some altitude sickness, or at least discomfort. (Wherever you go, I would certainly do some research on altitude sickness, because it can be quite serious.)
I would avoid Vail with kids and beginners. It just has too many places where green runs are crossed by blues and blacks, and that's a dangerous situation for beginners. It's also pretty cumbersome to get around. Beaver Creek (which we have not skied) is in the same general area and is much more family-friendly.
The Aspen area is a great place for beginners if you go to the right spots. (See
www.aspensnowmass.com ) Aspen Mountain and Aspen Highlands are the wrong places for beginners, but Buttermilk and Snowmass are nearly perfect.
Buttermilk is 3 miles from downtown Aspen (with frequent and easy bus service) and it is almost exclusively an uncrowded beginners mountain.
Snowmass is 9 miles from Aspen and is a huge mountain with all kinds of terrain. It has some of the best beginner skiing I've ever seen and a great ski school -- starting with 2 year-olds. There are very few advanced runs crossing beginner runs and it's a great place to start.
I have not skied Steamboat, but everyone I know who has raves about the place. It's also quite family-friendly, from what I've heard, so I'm sure there are good kids lessons there.
We have also not skied Squaw Valley, but we've been to Lake Tahoe and visited Squaw Valley several times in the summer. My impression of SV is that it's really a long way from anywhere. It's in a rather isolated area, with nothing around except the things in Squaw Valley itself. It looks like a great place to go if all you wanted to do was ski.
If you narrow your choices down to specific hotels, I'm sure someone here has stayed in them and can give you good hotel-specific advice.