As a guy who doesn't usually like skin tight clothing, I can only answer a little.
turtledove: what is the long sleeve top you wear made of?
Some fabrics, like cotton, when they get wet, switch from being good thermal insulators (which is good for staying warm) to being good thermal conductors (which you don't want, to stay warm). That makes them poorly suited for conditions where you sweat.
Another example of that is down.
Light plastic piles or fleeces (I like polyester, but there are other materials) are, for the most part, just as good thermal insulators as wool, and weigh a lot less, and almost as good as down, but stay pretty good thermal insulators when wet.
Instead of wearing the fleece under your leggings, could you try wearing them over the leggings? Fleece can move around a lot, so I wouldn't think, properly used, it would interfere much with motion, but if it is confined under elastic leggings, I wonder if that effectively adds high friction layers within the fleece? Could any one else comment on that?
However, either way, I wonder if the thickness would matter from an appearance perspective. Figure skating is to a significant extent an appearance sport. People like to be able to see how your muscles move, and anything thick could interfere with that.
The diving and paddling communities sometimes use "dive skins", made of stretchable materials like spandex, which are somewhat thicker than most leotards and leggings. They tend to breath less well than leotards and such, which makes them warmer, and they are designed to insulate well when wet. Some of them cover everything but your heads. I've never seen anyone skate with them, but I wonder if they might work fairly well. Though maybe they would be overkill, and might not be as easy to move inside of as a leotard. Of course, as with leotards, they hide very little of your body shape, and may even emphasize it, so if you are modest, they won't work. (As a modest guy, I've used them while paddling or swimming in somewhat cold water, but with a bathing suit on top.) I think they are more expensive than leotards. So it would be understandable if you didn't want to risk the cost for an experiment.
As other people have mentioned, silk is a great thermal insulator. So is polypropylene, though it may retain more odor - though there have been attempts to add materials that help with that. Both silk and polypropylene are fragile and heat sensitive, so it is best to wash them on a gentle cycle (or hand wish) inside a mesh bag, and to hang dry, or gently dry them on low heat. Both of these can be bought at places that sell performance outdoor wear, like camping goods.
Many skaters and other athletes take of layers as they warm up, and put them back on while resting. Zippered tops don't work as well as that, but as others here have noted, they help. Some performance outdoor clothing uses "pit zips" - zippers under the arms, which help a lot too - but AFAIK, no skin-tight clothing suitable for skating is like that.