That's a really interesting project you've got there! Freshly milled oak can definitely give you a beautiful, rustic look for outdoor furniture. However, keep in mind that green wood is going to have a higher moisture content and will be prone to warping and cracking as it dries. If your client is fine with that sort of natural, evolving aesthetic, then go for it!
For an added touch, you might consider using some mod podge fabric techniques to create custom cushions or accents for the furniture. It's a fantastic way to add some color and make each piece unique while still maintaining that rustic feel.