Nagato wins, almost every time.
Hashirama needs to bring out his Statue of 1000 Hands in order to threaten Nagato, which in turn needs him to enter Sage Mode. Both requirements on their own take more time than what Nagato needs to use any of the Divine Path, Animal Path or Armour Path, so I don't think Hashirama will get the time to do so.
The Animal Path in particular will apply immediate pressure with the Cerberus and Panda and any two other summons.
By the time Hashirama even gets free, if he does, the Armour Path will have brought missiles upon him that will surely kill him, as there will be nothing left to regenerate from.
Supposing Hashirama does indeed survive, his regeneration will be costly and he won't achieve much against four giants, two of which are immune to his physical attacks. He'll end up taking repeating fire from Armour Path, exhausting his chakra before long.
Supposing he somehow gets past all that, then by the time he does any random summon will suddenly crash upon him at the speed of a meteor. Nagato will have prepared this at the start of the match, when the other four were summoned.
Supposing Hashirama somehow survives that, Nagato will have managed to get close and absorb all his chakra with the Ghost Path.
Supossing he somehow survives that, then the chakra rods will disrupt him and allow Nagato to easily kill him by controlling him and then . . . Well, anything really.
There's also the Human Path which can't be beaten easily. Supposing Hashirama has the necessary will power, then Nagato will again have free shots at him during the struggle, particularly with the summons.
Supposing Hashirama survives that, and even enters SM, Nagato always has a 50-50 free shot with the Hell Path, which can kill through a simple lie detector test that seemingly cannot be resisted.
Supposing Hashirama survives all that, then it's clear that the fight was predetermined to have him as a winner and nothing in the world can defeat him!
