There are solid state relays which can be driven directly from the Arduino.
Search for "SSR-25DA".
There are simple humidity sensors, like the DHT11 and the DHT22, see the playground section: http://arduino.cc/playground/Main/InterfacingWithHardware#envhum
To accurate measure if it is raining, perhaps you could use a rain measering device from a weather station.
This method is not very reliable : http://www.youtube.com/watch?v=E6VSQThHkSM
The sensor could get dirty, causing it to think that it is raining.
There is a lot information about rain sensor, like this one: http://arduino.cc/forum/index.php?topic=73001.0
I like this one : https://www.sparkfun.com/products/8942?
It has a self-emptying bucket type rain meter. That seems reliable.
Edit: I think I misunderstood your question. Your goal is to measure the rain, and not to turn on a heater ? So you only want to detect if it is raining or not, or do you want to measure the amount of rain ?