As long as your horses don't get fractious to where they start doing their own version of mud sliding and there's a high spot for them to get out of the water/mud, leave them have the paddock.
I have lived in places where the paddock flooded. You can fix it but it takes labor on your part and working in the rain every day
Study the water and see where it thinks it wants to drain. Water ALWAYS finds its own path.
As long as it wants to drain away from the house and other buildings, take a garden shovel (pointed) and make a trench from the puddle to outside the paddock. You will have to do that every day, since trenching by hand with a shovel, is not a permanent solution.
If the water isn't showing you where it wants to "run off" to, then you pick a path for it and keep that path open.
It does work because I've done it enough time in my years to know it works; just have to be willing to get out there and get filthy sloppy soaking wet dirty and take your clothes off on the back porch