Good question. Finding a pair of gloves that will work well across different activities can be a hassle. But I’ve found a handful of gloves (so to speak) that can be used for basically anything.
My do-anything gloves for spring are REI's One Gloves ($36). They're made from a softshell polyester fabric that resists wind and water and offers decent warmth. I wear these cycling in March and April in the Pacific Northwest, and they're good in temps down to the upper 30s. For higher-intensity activities like hiking or cross-country skiing, you can wear them comfortably to freezing. Leather palms offer a bit of extra durability and grip.
Another great option is Manzella's Silkweight Windstopper glove ($35). I was initially skeptical that these would be warm enough—the material looks ultra-lightweight—but Manzella made them with Gore Windstopper, and when hiking or climbing, my hands have stayed comfortable into the upper 20s. For a little extra warmth, they work well layered over a pair of silk glove liners. My only gripe is durability, as they seem to wear through after two years of use.
And don't forget Outdoor Research's Gripper Gloves ($49), which are made from Gore Windstopper fleece, a warmer fabric than the material used in the Manzellas. The Grippers come with a synthetic fabric on the palms that makes them ideal for swinging an ice axe (or a wood axe), or poling on skis. They're one of the finest all-purpose gloves I've tested.