Prolonged changes in El Niño and La Niña events in the Pacific Ocean can seriously disrupt rainfall creating either too much or too little rain various regions. The Indian Ocean has a similar system called the Indian Ocean Dipole. All this can have serious implications for east Africa, southern Asia, Australia and North and South America.
Land salinization occurs when salt from below the surface of the Earth is brought to the surface by excessive land clearing for agriculture and the water rises bringing with the subterranean salt, as has happened in many parts or the world that have cleared land for agriculture. The other cause of land salinization is the over use of irrigation for agriculture, as occurred in Mesopotamia. All agricultural "fresh" water contains small amounts of salt which accumulates in soil over time. Land salinization results in the loss of vegetation and land cover. Large areas of land salinization have resulted in desertification and aridification of regions.
Regions that are normally dry can go through a "pluvial period", that is, one of increased rainfall, in which they green up. When the ice retreats, the rain goes away and these areas become dry again. The Sahara and the western US are great examples.
Similarly, areas that are wet in a warm period can become dry during an ice age.
Glaciation also causes a sea level drop, ans subsequent changes from meltwater and isostasy, and this makes ocean currents and littoral climate zones move around.
Finally, the ice sheets themselves can be as rainless as Antarctica, which has sometimes been called "the biggest and dryest desert on Earth". The Dry Valleys of Antarctica are the dryest ice-free areas on the planet.