Ice types are immune to damage from Hail persistent effect.
Ground types are immune to damage from Sandstorm persistent effect.
Rock types are immune to damage from Sandstorm persistent effect. Their Special Defense also increases.
Steel types are immune to damage from Sandstorm persistent effect.
Some pokemon have abilities that increase their stats depending on the whether. Examples would be Swift Swim in Rain, or Sand Veil in a Sandstorm.