The game makes it quite clear that adverse weather affects the Shadows in Mementos, whether it makes them more likely to call for backup, have Treasure Demons appear, or enter the battle despaired. However, the fact that it specifies the Shadows in Mementos led me to believe that it only affects those Shadows.
While rushing through the third Palace on a rainy day (no one was available to hang out, so it seemed like the best time to go), I encountered 3-4 Queen's Necklaces, which is roughly 3-4 more Treasure Demons than I usually encounter when exploring a Palace. I know that Rainy days increase the chance of rare Shadows appearing, but I thought that was only for Mementos. Does the weather affect Shadows in Palaces, as well?