In Minecraft, is it possible to customize your skin in single-player mode (not just in multiplayer)? How?
Yes it is possible. Multi-player and single-player modes use the same skin. Create or download your skin, then upload it by logging into minecraft.net, and selecting the Profile link.
Since there's no reflective surfaces in Minecraft, the only way to see your skin in single player is to go to third person view by pressing F5 (and again to switch back to first person view) or simply opening the inventory.