Sorry that this isn't what you're asking, but do you need to add anything? I had a trail through my woods at my old place that was driven on about 20 times a year. Where the tires compacted it, nothing grew. It was in the shade so barely anything grew in between the tires. So a quick run with the mower would keep that stringy growth from being a nuisance. Just a thought.
If it's due to mud, I'm not sure what the best option is so I'll leave that up to other advisors
