For running or high-activity workouts in moderately chilly weather, your hands will probably be happy with thin gloves made from moisture-wicking fabrics from most sports apparel manufacturers.
When the temperature drops to the single digits, look for gloves made from Gore-Tex or a similar wind- and water-resistant material if you will be outside in the sleet or snow, or fleece gloves or mittens if you anticipate being cold but not damp. Layering a thin pair of gloves under wind- and water-resistant keeps your hands especially warm and dry, as the extra layer traps more heat.
In my experience with wintertime running, removing your gloves as you warm up is another way to vent and “let off some steam” if you start to feel too warm. Put the gloves in the pockets of your sports jacket or carry them in your hands and put them back on again if you start to feel colder.