Yes, I hate the word koozie. It's a horrible term. However, sometimes you need some insulation on your burning hot coffee cup as to not squeal and throw your full drink after picking it up, and there's not many other words that come to mind. For this post, I'll still call it a jacket out of principle.
I like using half-pint mason jars because they are easy to find, inexpensive and easily replaceable. Classic look and a good size, but not good for hot drinks. Here's a quick way to save your delicate hands and make something fun too. I put a quick lesson together over at Design*Sponge with the full details. I talk about some new tools, and if you're wanting to do any leather crafting, they are a few that you should own.
Have a look, and maybe you'll want to give it a try. The techniques can be used to jacket plenty of other things too... beer cans, tennis ball cans, yogurt cups, tobacco tins?