Not necessarily. Infantry can withstand cavalry if they are properly positioned and can keep their formation. However, in mobility the Gondorians would be at a disadvantage. The best way for cavalry to defeat infantry without taking a lot of damage is using horse archers (i.e. Mongolian tactics). However from the description in the book that was something the Rohirrim were not big on. Eomer is described as only having a few horse archers in his company, which I would take to be typical of their armies.
If it were me, I would not fight the Rohirrim out on the open plains at all if I could help it. I'd march my army carefully along, building a series of fortified camps to protect my road. My target would be the cities and settlements of Rohan. I'd pick them off one by one until I had cut the economic base out from under the Rohirrim. At that point their eventual demise would be inevitable.
It's slow and not very glamorous, but effective.
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...finding a path that cannot be found, walking a road that cannot be seen, climbing a ladder that was never placed, or reading a paragraph that has no...
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