OP, you did not specify if your original tires are a load range "E" or load range "D". Or a load rating number (Something like 120 or 125, etc...). Need that information to determine if a given new LT tire will have the same or better load handling.
If you originally had Loadrange "D" ST tires, then LT235/85R16 Load Range "E" should be good enough as many of those tires have a similar weight capacity (load index of 120 or higher).
If you originally had Loadrange "E" ST tires, then each of those ST tires were rated at 3,420 lbs a piece. If you wanted to go LT, you'd have to step up to something like Goodyear G614 RST's which are load rated "G" at LT235/85R16. Pricey tire, but they are rated at a superior load. Then you also have the issue of whether or not your rims can handle the load range "G" pressure (110 psi). Or another alternative is to go to an even taller and wider tire, like something with a load rating number of 123 or higher (roughly 3,400 lbs). an LT265/75R16 can achieve this, but you're looking at a tire that's 1" taller, 1" to 2" wider and require a rim at least 7" wide compared to your current ST's, so I don't know if you can go that route depending on how wide your rims are (most trailer rims are about 6" wide, but some are made at 7" wide).