All: Some loss of health if exposed to the elements too long.
Rain: Decreases time it takes to farm. The more water plants get, the faster they'd grow. Increases time for other projects (outside).
Snow: Increases time it takes to farm. Travel time would increase.
Hail: Minor damage to characters and cars.

Heat: Increases time it takes to farm. Plants would need more water.
Cold: Time required for all outdoor projects would increase.
Thunder Storm: Random lightning strikes, affecting character health and building durability.
Sand Storm: Affects character visibility. Maybe they can't travel during one.
Hurricanne: Same as Sand and Thunder, only that winds would affect things.
Tornado: Possibility for random major building damage.
That's about it for what I can think of at the moment. And I'm sure they would all affect animals in some way. Maybe they'd hide like someone suggested before.