In a war between USA and Russia who would win no nukes?

If you mean only the USA and Russia (not including us allies) the USA because it has a technological upper hand by far plus Russia hasn't got a great navy either. USA is #1
What kind of war doesn't have nukes. Russia would win with nukes.
If nukes are ever used between the 2 - NOBODY wins. The devastation to not only the two countries but the collateral damage to the rest of the world would likely cause a complete collapse of civilization.
Who would win in a no-nukes war would depend a lot on where the war was fought. Each country would have a distinct advantage fighting on their own home turf. Napoleon and Hitler both found out how foolish it was to try to fight Russia in Russian territory.