Aside: An igloo is not a home. It’s a temporary camp shelter for use on hunting trips.
Does Siouan have an official written version, and does it use the Latin alphabet?
Arguably… so are some types of wickiups and wigwams.
As far as I can tell, there is no “official” version, but there are several more common versions. The oldest is called the Riggs alphabet, named after one of the missionaries who devised it in the early 1800s. Ulrich and Deloria are two other variants.
Here are a few different variations:
http://www.languagegeek.com/siouan/y_dakota.html
Most of them use mostly Latin-ish letters.
Again, this comes from Mr. Google. I am not an expert on the Siouan languages by any stretch of the imagination.