Depending on which 38/15.50 you should be fine on a 10" wide wheel.
I know on Dick Cepek Mud Country and Mickey Thompson MTZ you pretty much need a 12" wide wheel since they are the widest 15.50 tire I've seen and you get a lot of sidewall flex if you mount them on 10" wide wheels.
I run 38/15.50R20 DC Muds and thought they were fine on 20x10s, but now that I upgraded to 20x12s it drives/rides/handles much better.