On my old hills course with heavy clay soils - we got (well, they still get) 35" of rain a year, but most of it is in winter (we play year round). Evaporation is low as the weather is often cloudy/foggy/misty. There would be many days of high humidity but no rain, and no evaporation. Micro-climates are important with clay soils.
The points raised above about ensuring trees don't shade wet areas, and that winds are allowed to assist with removing excess moisture are also important. As is a planned drainage system (trunk mains, not the web-based strip drains) that shifts water from the top end of the course to the bottom,or to dams. They can be open streams or large pipes. But they need to be well planned to collect and shift the surface water that gets shed in a downpour.
Slit drains can be effective, but the movement of water through heavy clay can make them a slow process - they stop an over-water-logged course but won't prevent a soft course. You need to understand the two rates of movement of water in the particular clay. I was told our clay moved at 1mm an hour down, but only at 0.1mm an hour laterally.
So, after a downpour, any water not drained at the surface can get into the soil at 1mm an hour - not too bad. But, if the soil below the surface is waterlogged (because of thatch or because of over-watering in the autumn prior to the wet winter) then you might only get to shift some of the water. It could take quite a while for the water in the clay to move laterally to the slit drains.
I'm sure others with genuine turf experience could explain this better, but the severity of the clay in terms of water speed movement vertically and laterally, coupled with the local climate, potential for surface evaporation, surface drainage and closeness of trunk drains will all contribute to the final outcome during wet weather.
James B