Heres a word for you, well, its not really a word. More of an acronym: GtW - Gandalf the White.
He is by far the absolute most important thing in this matchup. He is basically the Anti-Rohan, so use him well. This is a upgrade rush to counter anything Rohan has and Gondor should always get upgrades faster out of the the two. Armour and Blades are vital in this matchup especially so you will be able to guarantee GtW power points. After upgrades and 4 horses you will be able to maintain map control and ensure when Gandalf is out you will have a clear cut edge, making sure you put Rohan under some enormous amounts of pressure.
Rohan has many strategies available to her, all of them involving fast Rohhirim creeping the map. Fast ugrades, Fast ents and Fast upgrades to Aragorn are all possibilities you must be prepared for. Peomen and Elves don't really become much of a problem if you have Gandalf, unless they're supported by heroes.
