I also recommend the Goodyear Endurance in load range D. Second choice, Carlisle Radial Trail HD, also load range D. I run the Carlisles on my Scamp
because the Endurance doesn't come in a 13" size.
Both are ST (special trailer) tires with radial construction for good handling, smooth ride, and no flat spots on a cold morning. I run bias ply tires on my utility trailer, where handling and ride are less important.
But... if it's just going to sit all winter, why buy the tires now? I'd wait and get fresh ones a few weeks before your trip. Age and exposure are typically what kill trailer tires, not miles (unless you travel a lot more than average).