If you're having trouble with huge trees, see this thread.
At Hard/Very Hard battle difficulty, the AI gets boni in morale and defense, if not more. At Hard/Very Hard campaign difficulty, the AI will get increasingly stubborn and usually concentrate its forces solely on wiping the human player out.
And yes, trust your infantry to fight. They do a marvelous job (and I finished conquering the whole of the Iberian Peninsula about two weeks ago).
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