Do your herbaceous peonies for back completely in your winter, Lola? Unless they're hit with something bad like a hail storm or fire, something that kills back all of the growth, peonies will just sit with no new growth in warmer climates and never really go dormant. They need that dormant period for best performance so if they don't get it naturally you'll need to help them along by cutting them back to the ground in your fall, once the days have started shortening and the worst of the summer heat is gone.
In an area that doesn't usually get below 0C they do need to be planted shallow, tops 2cm or less below the surface and no mulch. Your situation with wet winters is a concern, raised beds or some means of artificial drainage would help a lot, sitting in water when they're dormant will cause rot.
It's always a good idea to test your soil so you know what will grow best for you. That said, I've never tested mine but know from what grows well that mine is slightly on the acidic side. Peonies aren't incredibly picky, have seen them grown in gardens with rhododendrons and blueberries with no amendments, but you'll have less health problems with them if you have neutral to slightly alkaline soil