Exercising outdoors in the winter is all about layering and choosing performance base layers can be tricky. Basically there's two main choices. Polypropylene or Merino Wool.
Polypropylene is a quick drying polyester fiber that wicks moisture away from the body. The fabric was engineered to do the wicking, since we all know regular polyester just makes you sweat. The downfall? The fabric retains odor, so even though you wash it, it can still smell a little stinky. Patagonia makes 4 different weights of its polyester performance baselayer called Capilene, so you can dress according to the temperature. They cost anywhere from $40 to $90.
On the other hand, Merino Wool is a natural fiber that's not at all itchy like that bumpy sweater your grandma knit you. When it comes to an active lifestyle, it keeps you warm in the winter and cool in the summer. The wool naturally wicks away moisture. Plus, it can be washed and won't shrink. The downfall? It's a little more expensive than "polypro." Smartwool makes a great long sleeved shirt for $75.
If you want to know which one you should choose, read more
Both kinds of base layers come in a mulltitude of different styles from short sleeves, to zip-ups, to hoodies. They make bottoms too, so you don't freeze your buns.
For really active sports that make you sweat like hiking, running, and cross-country skiing, I'd wear the Polypropylene. During less active sports, where you're stopping and starting, like downhill skiing or ice-climbing, I'd slip on some Merino wool to stay toasty warm.