One nation that has always fascinated me is the Khazars. For those who don't know, the Khazars were a Turkic people living in what is now Ukraine and Southern Russia. They were one of the major steppe invaders, following the Huns and Avars and establishing a nomadic empire that lasted centuries. What's really interesting is that between the eighth and ninth centuries the Khazar elites converted to Judaism. Unfortunately, the Jewish nomadic empire was conquered by the Rus, Pechengs and Cumans and their religious impact disappeared into the ever-changing melting pot of steppe cultures.
Now, I'm not interested in a way to get the Khazars to survive. This thread is less for 'how' than it is for 'what'. Specifically, if the Khazars had managed to spread Judaism to their subjects and neighbors, what would the resulting religion look like? Let's assume this Steppe Judaism spreads throughout the western steppe and at least around the norther shore of the Caspian. Some ideas:
Airag: Airag, or Kumis, is fermented mare's milk is one of the most popular drinks among nomadic cultures and their descendants. Unfortunately, horse meat isn't exactly kosher, and thus neither is its milk. Perhaps the milk restriction would be lifted in this version of Judaism. Or alternatively a cultural switch to cow milk could occur.
Wine: There are some Jewish ceremonies that require wine, most of them holidays. Since wine isn't exactly easily produced by nomads, this might need to get retooled. Perhaps Airag could stand in, or more likely wine would be discarded in favor of simple blessings over the bread.
Matzoh: Easy to make, easy to carry. Could be popular?
Warrior Faith: For more warlike peoples, an emphasis on the warrior kings of the Bible might be appropriate. Emphasize the military victories of the ancient Hebrews.
Israel: For a people with only religious connections to Israel, and not much ties to their own lands, it might end up that the importance of Israel as THE promised land might turn into it being A promised land.
Torahs and Arks: With the need to move with the people, Torah arks would need to be detached from synagogues and turned into portable altars.