Tread depth and weather cracking have nothing nothing to do with a tire's ability to carry a load, but age does. Back in their day, nearly all farm trucks had traction tires on the drive and highway on the steer. I don't think any American manufacturer makes a traction tire any more but something like a Samson Chinese tire isn't bad.
https://www.nebraskatire.com/truck Make sure you get what they call the mud and snow or open shoulder tire. A traction tire with a closed shoulder tire that is made for highway traction will fill up with mud and be just as slick as what you have now.
