I think I'd go narrower for better performance
I prefer to keep the trailer spare the same size as the trailer tires.
I agree and I agree.
My offroad trailer experience dates back to the mid 1960's, when my dad bought 7 wide wheels and Armstrong 11x15 tires from ******** Cepek when Cepek was just starting his offroad tire business in his garage. (Matched larger-than-stock wheels and tires on jeep and trailer is nothing new. The rationale then was the same - looks cool to have a matched set and one less spare.)
I didn't match my current trailer tires to the 35x12.50x15 BFG MT tires on my jeep because:
1. 35" tires are big, heavy and expensive. MT tires are appropriate for a drive axle; unnecessary on a towed axle. They add nothing to the trailer's ability to be pulled across any reasonable obstacle and make the trailer more difficult to maneauver by hand. Installing them on the trailer would also force me to modify the suspension and replace the fenders.
2. I remember two occasions, once deep in Baja and once in the dunes at Pismo Beach, when one spare shared between jeep and trailer wasn't enough. (Reason alone to abandon the concept forever.)
My solution:
I wanted the tallest tire that would fit the width of the trailer fenders using the stock suspension. That measured 31" However, every commonly available 31" offroad tire is a 10.50, too wide with a stock offset wheel because it would rub both on the trailer tub and the fender edges.
I went with military 7:00x15 NDCC tires on the trailer. Nearly 31" tall and 7.5" wide mounted. For now, I carry extra tubes and tire tools and can use the jeep's 33x9.50 spare in a pinch. I have an identical trailer spare ready to be mounted "just as soon as I get around to making the bracket for it."
You may notice that my jeep spare is 33x9.50 but it's tires are 35x12.50. (Largest spare that would fit my swing-away rack.) Although the spare is 2" smaller in diameter, it is a true offroad tire and not a "donut." It will get me off the trail and far enough down the road to get a repair or replacement without worries that it might not be up to the terrain or distance.
I am sold on the idea that jeep and trailer should each carry its own spare, and that the spare on each should be identical in size,
if possible, to the tire it is intended to replace. However, it is not always possible. In such an event, my preference is a real tire very close in size.