Cheap workaround would be to use a animated black & white grainy rain texture.
Something like THIS
You'd need more than 3 of these to keep looping, animating over the screen. You might need to make it have transparent backgrounds or use a effect to make it look like rain.
Next, randomly generate animated splashes on the ground.
Using particles and sprites are both going to be intensive and slow down your game greatly.. do realize we're not going to need so many things an object has for each rain drop like a unique ID for each rain drop spawned. For something as trivial as a rain effect, search for methods older games use and you'll find they mostly cheat for this effect.
You may also want to check this out,