Whatever you wish to call it, the Deadly Desert is not the only sandy desert environment on the Ozian pseudo-continent. Ruth Plumly Thompson was especially keen on creating desert domains, pretty much inevitably inspired by the Arabian Nights. The first clear example of this is the southeastern Munchkin kingdom of Mudge in
The Cowardly Lion of Oz, a land of silvery sands and date palms. The people dress in turbans and live in tents that they move around a lot, and the men have blue beards. The Mudgers used to make their living as raiders, but Ozma and Glinda put a stop to this by making them stay within their own borders under threat of decapitation. The book reports that the ruler at that time was the grandfather of the king in the story, so there must have been some turnaround at a time when death was practically unheard of. Maybe it wasn't uncommon for princes of Mudge to take walks alongside the Deadly Desert with their fathers. Regardless, at the beginning (and end) of
Cowardly Lion, the country is ruled by the hot-tempered King Mustafa and absent-minded Queen Mixtuppa. When Mustafa grows restless, his chamberlain Tazzywaller suggests hunting lions. This eventually turns into an obsession for the monarch, and he has 9999 and a half lions in his royal enclosure. The half is due to Tazzywaller being forced to cut one of the lions in half with his scimitar in order to save his own skin, which resulted in the front half escaping. With no more lions in Mudge, Tazzywaller's rival Panapee (what an unfortunate name) advises capturing the Cowardly Lion, and Mustafa ropes the newly arrived
Notta Bit More and Bob Up into helping him with this. Mustafa's folly results in his lions being turned to stone, and a giant stone man ending up in his makeshift garden. And that's the last we see of him in the series, although we're told that he sold a lot of his stone lions for use throughout Oz.
Hungry Tiger not only gives us the Evian desert dominion of Rash (described in some detail
here), but another desert area within Oz itself, where the winding road deposits Betsy Bobbin and Carter Green after dragging them around the land. This area has a patch of quicksand, and is where the Quick Sandals are kept. It's in
Yellow Knight that we next see another significant desert country in Oz, however. This is Samandra, located in the small stretch of Winkie Country to the east of Oogaboo. Samandra is a prosperous and well-established country, with some of its inhabitants being over 700 years old, but it is perhaps best known as the only part of Oz in which animals are unable to talk. It was also the original home of the Comfortable Camel and Doubtful Dromedary. As far as its history goes, the Sultan of Samandra allegedly feared an alliance between his two neighboring countries of Corumbia and Corabia if the prince of the former married the princess of the latter, so he transformed the Corumbians into trees, and the Corabians into fishes and frogs. They remained this way until the events of
Yellow Knight, and after they were restored, Ozma stripped the Sultan of his sorcery.
Wishing Horse once again uses a desert monarch as its main villain, but at least this time he's somewhat more sympathetic. King Skamperoo of Skampavia, a country adjoining Noland, tires of his dull and barren homeland, and uses some magic that he comes across to declare himself Emperor of Oz. He is eventually persuaded to return to Skampavia, only this time he has more sense, a talking horse to advise him, a greater willingness to listen to his prime minister, and some magic left to improve the climate of his own country.

I suppose it's also worth mentioning
Enchanted Island, which not only mentions the Desert of Ho-Taro as one of the neighbors of the wool-producing Gillikin kingdom of Kapurta, but also that the camel Humpty Bumpty was originally the favorite steed of the Shah of Hah Hoh Humbad. This place is described as a lazy desert city in the Munchkin Country, not too far from another city called Drumbad. It seems that many of these Ozian desert countries are located along the edges of the Deadly Desert, which would make sense. Kabumpo even comments in
Silver Princess that "[a]ll the countries bordering on the Deadly Desert are queer no-count little places." This isn't entirely true, however, as the quite pleasant Jinxland also borders on the desert. It doesn't appear that the destroying sands have the power to enter Oz, but they can perhaps affect some (but not all) of the nearby climate.
