It might not even get to Mokuton since Hashirama will most likely engage in taijutsu first since Minato will run at him with inhumane speed and he can't start sprouting trees when his opponent suddenly shunshins one inch from his face. Even if he dodges with only needs place a kunai near him to end him before he can react as Tobi, A, random Iwa nin couldn't react in time to do anything. Minato's style in war didn't give armies a chance to do anything. Why would Hashirama(one man with no spectacular speed) get a chance?
Alright, now the next argument would be if Minato can actually kill Hashi in one move because of his medical techs. Can one regenerate a cut off head? I think not. Even if Minato fails to kill him in one attack, Minato will mark him somewhere in his body he can't notice then teleport and try again...and again and again and again.
Now imagine if Hashirama, by some unbelievable twist, prevents Minato from closing the distance between himself and the Senju(something no shinobi has ever accomplished...ever) and actually gets the chance to create trees. Minato can summon large toads who can jump over it and close the distance between Minato and the Senju so that Minato can kill him. Minato can also protect Bunta from Mokuton by using the Space Time Barrier to warp away incoming attacks.
Obviously Minato still has many obstacles like the Bringer of Darkness that the Third couldn't break and the Mokuton clones which can merge with wood to hide themselves making it very difficult for the Yellow Flash to find the real Hashirama but my point is simply this. If Hashirama wins, it won't be easy. Minato all has barrier techs(he alluded to this fact when he teleported the Kyubi out of Konoha, he said 'I got to put up a barrier' but then Kushina did it and he was worried she was overdoing things) Barrier are powerful since a C-Ranked one could withstand a direct punch from Guy's 5/5 strength, Obito's could withstand a direct punch from the Eight tails and Kushina's could withstand Enma(who was once used to tear Mokuton to shreds with ease) so Minato having barrier techs will provide excellent protection from Mokuton. There's also the fact that Minato is known to Pa and Ma so the possibly of him being able to put them to use remains.
My point-its gonna be exceedingly difficult for Hashirama to win if he actually can.