Read this. The best time to fix a muddy run is when you build it.
Pat’s Big Ol' Mud Page (fixing muddy runs):
https://www.backyardchickens.com/web/viewblog.php?id=1642-fix-a-muddy-run
There are two basic ideas, keep water out to start with and get water out after it gets in.
With the ground being sand you are better off than any other soil type because sand drains so well. But if water stands there you still have a problem. You don’t want your coop or run where water drains to it, you want water to drain from it. The water has to have a place to drain to even if the soil is sand. Otherwise you have a sand-filled bathtub.
The problem is that chickens poop. That poop gets in the soil and rots. So far no big deal. What causes it to rot is that organisms eat it, just like composting. If it is dry enough those organisms are aerobic (oxygen breathing). Those don’t smell. But if it is wet the organisms are anaerobic and those can turn it into a smelly mess pretty quickly. It needs to stay dry or dry out quickly enough that the organisms stay aerobic. It only takes two or three days for the anaerobic to start to take over and the smell to start.
One thing Pat does not mention is chicken density. The smaller the coop and run the less space for them to spread the poop. The bigger you can make the coop and run the more space they have to spread the poop. That can help a lot. A poop board in the coop can help keep the poop build-up down in there to help prevent this problem. If poop gets thick enough it can hold moisture and cause this problem. Instead of looking at how tiny can I build, look at it as how can I provide enough space for the number of chickens I want, then build it a little bigger than that. Extra space helps in a lot of ways, not just in keeping the smell down.
Pat sort of refers to this but in most runs the chickens will destroy practically all vegetation. Again it’s a matter of chicken density but also climate, seasons, and type of vegetation. Chickens eat a lot of green stuff and even scratch out the roots and eat those unless they have a lot of room. Unless you have a huge amount of room per chicken (most people don’t have room and if you cover it, it gets extremely expensive) don’t worry at all about planting anything in the run for them. They will destroy it. Your run will be bare. You can build a tall frame, cover it with wire, and grow stuff they can eat once it grows tall enough without them destroying it, but that is limited space. Count on your run being bare of vegetation.
Good luck! Now is the time to look at this.