Well, we have hilly, rocky terrain and some red clay around here, minus your rain! My gelding is about 17.3+, 1800 lbs. + and he handles himself very nicely around here, going up and down hills, around hairpin turns, etc. Once when we were by a river, his front end went into quicksand. He turned around and then his hindend went down up to his belly. He heaved himself out, blew his nose and off he went. I can say we are vertically challenged when it comes to riding under wooded areas!
He has nice big feet which might be an advantage for traction :)