Scott, if you can make a lager, you can make an ice beer. You just make a lager you like, and partially freeze it and filter out the ice.
Generally speaking, it's a bit easier to brew an ale than a lager. So if you aren't already a brewer, I'd suggest you start with brewing lighter ales. Just as with wine, you can buy kits that have all the ingredients you need to make your own. Most people start with extract kits. Anything described as a "cream ale" will be light and not very bitter or hoppy. Just read the kit descriptions on sites like Austin Homebrew Supply or Northern Brewer, et. al.
On the other hand, if you have a spare freezer, you can convert it for lagering by plugging it in to a Johnson Temperature Controller
. Then you can brew something like this Molson Ice
There may well be other ice lager kits out there, I haven't looked. If you like brewing and decide to go "all-grain", which takes a considerable investment in equipment and some experience acquired over time, you can make any style of beer you like.