Is it possible to do the trail when it's raining? If yes is it still recommended in wet conditions?

I would even recommend a light jacket or rain coat on a sunny day rocks drip along walk ways I'm glad I was there in a warm day because we got quite wet

It is possible if is not raining hard. A good raincoat and pair of sneakers will do.

It's always wet there in the trail due to the over spay of the falls

You can do the trail in the rain, the stairs and trail are damp in parts either way from the waterfalls, but with heavy rain I would expect the trail to be very slick. Wear some sticky shoes and watch your step.