Why do you want a subpanel? 1.3x3 = 3.9A which is not nearly enough to need to worry about a subpanel. If all we are talking about here is the three waterers save the $ you would spend on a outdoor rated subpanel, ground rods, etc and just run 12 gauge to the three waterers and use a 15amp breaker. (I'm assuming these things are just something you could plug into a standard outlet). There will be a voltage drop, but not enough to matter on such a small load assuming you have 120V at the barn with the same live load connected.
If you are concerned you may be using these outlets for something else in the future you should pull #10 and use a 20amp breaker. That will bring the voltage within more tolerable limits at full circuit load.
Use 3/4 inch conduit with THHN stranded wire (not UF) and 18"depth for the conduit is good.