I think a grass arena would be a wonderful idea. In our sand arena, the grass growing just outside the arena tends to creep into the edges of the arena. My horse always hugs the rail so that he can step on the grass parts. I think it's more cushioning for him.
Plus, the dust reduction would be nice. So, unless you're in a really rainy area that would make it slippery too often, it sounds like a great idea! Although, I don't ride outside in the rain anyways!
Just be sure you pick out a nice, flat spot and maintain the footing very well. If you put up jumps, be sure to move them around a lot so you don't wear out the ground at the popular take-off and landing spots.