I get asked this question a lot! It depends a little bit on who you are and what you're doing at the rink. For a child beginning lessons I recommend layers of athletic style clothing.Thick leggings (consider tights underneath) sweat pants, jogging pants, or hockey pants are all great options. I do NOT recommend wearing jeans or khaki style pants as they are not as warm or water resistant. A t-shirt or turtleneck with a jacket or sweatshirt should suffice for the top layer. A heavy winter coat may restrict movement. Gloves should be considered a must, cold hands are a distraction and gloveless hands can make falling and getting up pretty miserable. Long scarves can be a safety hazard, shorter 'infinity' style scarves or neck warmers are ok, as are hats or ear warmers that are secure. As tempting as it may seem to wear thick or wool socks, very thin socks or tights should be worn with skates to help prevent blisters and allow feet to feel weight transfers. Skates should fit snug and be tied tightly to provide support. Helmets are optional, but recommended for young skaters.
For the more advanced figure skater there are additional factors to consider. For one, you'll probably be spending more time on the ice. Adding an extra layer may be helpful, also opting for moisture wicking clothing becomes important. There are pants and jackets designed specifically for figure skaters and though they can be pricey, they really are warmer and more waterproof. The more advanced you become the more you will need unrestricted movement and form fitting clothing that will not get caught up on anything. If you are a skater who is planning to participate in competitions or shows you will at least occasionally want to practice in skating tights and a skating dress.
If you are a parent in the rink, bundle up! Natural fabrics or moisture wicking materials work best. Layer up, wear thick wool socks and boots, top it off with a parka and grande coffee! Bring a blanket or two (one to sit on) If you get too cold walk laps around the rink to warm up!