Well, since I'm going to be a nerd and go into a little bit of analysis with this...I'll state who I think would win.
There are several things that come to mind when thinking which race would win in a war. The main four being terrain, stamina, speed and strength. So here goes...
Terrain:
It depends on what terrain the war is set on, as I am sure that Zora's need a large quantity of water to survive for extented periods of time. Whereas the Goron's need a certain type or rock to feed on, although, the can eat other kinds of rocks, but they prefer the type from the Dodongo's Cavern.
If the terrain is plentiful in water, the it is most likely that the Zora's would win, as if the Goron's go into the water, they are greatly outsped. Unless, they drown of course, but evidence of a Goron surviving under water in Twilight Princess leads me to believe that they can do so. Anyway, they wouldn't be able to land a hit, as there attacks would be slowed even further. However, their running speed would be greatly increased, much like when Link goes underwater wearing the Iron Boots. That would be at the cost of their attacks being slower and having less power though, as there would be more force going against there arm than when they are in the open air.
When I was thinking about the above, I was wondering whether or not the Goron's need air to survive or not. In Twilight Princess we find a Goron that has survived in the water for a long period of time in the Zora's Domain. Whereas in Majora's Mask, if you fall in the Water whilst wearing the Goron mask, you respawn. I do think that is mainly for gameplay, as it would be a pain in the *** for you to have to get out of the water, especially in some areas.
If the terrain is dry, then the Goron's have the upper hand as they are more likely to find rocks than in wet areas such as a lake or an ocean. The Zora's would also be out of their preferable grounds, and would need a constant supply of water to keep themselves in shape. They'd be even more screwed if they were on Death Mountain, as the heat would cause them dehydrate even quicker than normal. The Zora's speed would also be greatly decreased, making it harder for them to attack the Goron's and not get hit themselves.
Now that the bulk of my post is over, onto the smaller parts.
Stamina:
I don't think that there is any in game evidence for this subject, therefore I will have to go of what I believe.
As most games and films stereotype, big bulky beings usually have a high stamina than those beings that do not hold any bulk, along side a high tolerance of damage to the body. Thus, I believe that Goron's would have the stamina to take a large quantity of hits from the Zora's. Whereas the Zora's would only be able to take a small quantity of hitsf rom the Goron's.
Strength:
This subject is extremely similar to the subject above, in terms of bulkier guys having superior strength than those that are not. There is a lot of in game evidence for this though, as we can see that the Goron's are very strong from some of the things they do in game, and they also mold their items around strength. Such as Sumo Wrestling and Bombs, both of which are better when more strength is involved. So once again, the Goron's hold the advantage here.
Speed:
Speed is something that almost all physical activities rely heavily upon. The higher your agility the better you are at many physical things, especially when it comes to fighting and war. This advantage easily goes to the Zora's, which is backed up by Majora's Mask when you play it. You move considerably faster as a Zora on land than a Goron if I remember correctly, and when underwater there really is no competition.
Speed also overcomes the other two sections above fairly well to, as with speed it is rather easy to dodge slow attacks, and then deliver them before being swiped at again.
To be honest, it would be rather close, but I think that the Goron's would win if away from water on any terrain, even those that aren't their own environment. Whilst the Zora's would struggle outside of their own environment.