I love the idea of painting it all green, trim too. Here is an example, though perhaps lighter than what you had in mind. Remember to factor in how the color looks against your roof and the unpainted wood parts.

I like Kendrah’s suggestions. Using a subdued green would look great with your natural wood touches.

The existing highly-contrasting trim color seems garish to me.

Thanks!

Any color that isn't light will look sharp with white or cream trim. If you want a more monotone look, I'd have the trim be a different shade of the same color. If you paint a dark green, then the trim could be the same color with 50% or 75% more white. If you paint a medium-ish color, the trim could be the same shade just darker.