Hi mdunlevy and welcome. The white wires are generally negative (sometimes called ground) wires. The green wires are probably 12V DC power to the running lights on the outside of the trailer.
I can't tell you if you should splice them or not. Where do each of the wires terminate? Do the other ends (not the free ones) go back into the trailer or do they seem to go to the front into the tongue?
Hi-Lo 1707T - Tire Minder TPMS on Tow Vehicle and Trailer, 300W Solar Battery Charger, Equal-i-zer WDH, Progressive Dynamics Converter, Fan-Tastic Fan
2014 F150 Platinum 4x4 3.5L EcoBoost SCrew