Yarn with a lot of "loft," eg, mohair, angora, loosely spun wool or anything fluffy and airy can be very warm even if knit loosely. Body heat gets trapped between the fluffy fibers and keeps you cozy. So you can have it both ways: lightweight and warm.
I find that many acrylics feel warm and cuddly when you first put them on, but after a while seem clammy. That's why I prefer superwash wool or acrylic-wool blends for baby clothes and blankets that must be both warm and washable.
Wool is a particularly good insulator. Woolen mittens will help keep a kid's hands warm even when they're wet with snow; in this case, knitting tightly does add both warmth and water-resistance.