It IS possible to make HD skins, but only on offline mode. I'll say no more, for I've already said too much. Edit the actual char.png files in the texturepack to be HD. Like I said earlier, it only works when you are offline. It doesnt work in Multiplayer.
Guys, do you know how to use the Google machine? 2 minutes and I found this: http://www.mccapes.net/index.php , it lets you upload HD skins to minecraft.net. Capes and ears too, but that's a bit trickier, it requires a mod, some file editing, etc.
Woah. If you want to make an image higer res, would you have to modify some of it yourself? Or is there some kind of tool which can be used to automatically apply relevant colors based on the colors available and on the skin? I have never used PhotoShop or any other sophisticated photo editing tool.
You can change what the default skin looks like to you, and change the resolution as you see fit. Some texture packs do this. However, this does not change your actual skin, it just tells the game to use your pic anytime someone's skin is set to 'default'.