The biggest thing that tots need is comfort. It's cold, slippery, and mom is inaccessible. They don't need need pads or elbow pads or giant mittens. The little stretchy mittens, a long sleeve shirt and a light sweater, plus jeans or sweats and snowpants, is a good outfit for a beginner in the 3 to 5 year old range. Don't put them in big bulky jackets as it's too hard to move. Don't tell them they are cold, or that they are going to be cold. It's not that cold in an ice rink if you're properly dressed.
Yes, I like to see tots in well-fitting, flat-back helmets (skateboarding helmets are the best).
Long sleeve shirt plus sweatshirt or warm sweater, pants in two layers--tights plus sweats or jeans, or leggings plus sweats. Again, light gloves, not bulky mittens (mittens are too warm, and it's hard to hold hands). Younger children are fine in helmets or a soft or padded hat. Please don't put your 6-year-old or younger in low rise jeans (whoever came up with this concept was an idiot). You would not believe the number of baby-butts I see in a week.
Learn to Skate levels, especially tweens
You're going to start getting agitation for the cute skating clothes at this level, and your degree of indulgence is entirely up to you. I like to see kids deliver the goods before they start dressing like skaters, i.e. mastering the first jump is plenty of time for the Chloe Noel pants. In the meantime, your upper body and gloves are the same as the prior two levels--long sleeve shirt plus sweatshirt (a zipper one is good at this level, for easy removal if they get warm), and stretchy gloves. Tights plus workout pants are great; you can get perfectly adorable yoga pants in any size at Target, for a fifth the price of the ones at the skating shops. Personally, it makes me insane to see some Delta or even low freestyle skater in $150 worth of skating clothes, especially when parents then turn around and complain about the cost of lessons. That's 5 privates or two 10-week class sessions that kid is wearing.
At this point, your skater is committed and needs to start dressing the part. Hair combed neatly and pulled into a high ponytail. Yoga or skating pants, or skating tights and dress (you can get inexpensive ones at resale or a Big Box store, or specialty ones at a specialty skating store). Skating pants are usually a little longer than ordinary yoga pants, or come with stirrups or other skate-specific details. Let your budget and frou-frou tolerance guide you. But at freestyle the coach needs to be able to see the line of the skater's body, so body-skimming styles are best.
Some places to get nice specialty skating clothes are Rainbo Sport Shop, Chloe Noel, and Seku Skatewear (my favorite, but oy, the prices).
Years ago at one of the rinks I work at there was an unspoken rule that only freestyle girls wore skating skirts. As time went on, younger and younger, and lower and lower level girls started wearing skating skirts. Low and behold, the high level girls all started wearing pants instead. Now everyone's in pants. I'm waiting for the high level girls to reassert their preeminence and switch back to skirts any day now.
What do you like to wear, or to put your kids in for skating? What are some places to go for good skatewear?