Can I splice and extend feeder wires to a barn?
Since you are pulling in conduit, you don't need a full blown box for this job.  Simply use an appropriately sized, weatherproof conduit body (a Type C is what you want, by the way) made from the same material as your conduit.

However, you will need to use the 314.28(A)(2) rule that the body must be no shorter than six times the distance from the entrance to the opposite wall/exit in order to size the body correctly, as you are splicing 4AWG or larger conductors in the body.