For the ice and snow maybe Permafrost, or anything with the prefix 'Yuki-' which is Japanese for snow.
For a desert maybe Aleabur, which according to google is Arabic for Crossing, or use an Egyptian god or goddess like Osiris, Annubis, or Bastet. There's a whole list of different gods on wikipedia. A lot of times I find using a foreign language to be useful when it comes to naming things.