Nutrient availability and rain don't necessarily go together: Tropical Rainforests are particularly nutrient-poor.
Vburmester - Many gymnosperms (pine relatives) from wet, warm climates do indeed have larger leaves.
For the same leaf mass, one that has a smaller area is longer-lived, and may therefore be less costly in the long run. If plants are slow-growing they are more likely to have hardy little leaves that they don't need to keep replacing.
Large leaves heat up more, but also cool down more. If keeping leaf temperature around air temperature is less likely to cause heat/frost damage, leaves will be smaller.
Maybe they have enough light and don't need to put out more leaf area, because other things than light limit their growth.