Flying units will work just fine, like they do in a siege.
But here's one more complication: When that water global turns the oceans to ice, can all units just walk on the ice? Also cold scale +3 might mean ice too.
And I want that cool battle spell from LOTR that makes the river wash the nazgul away .
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All the problems you listed can be easily gotten around. The real problem is whether the game can be coded to select the battle terrain based on crossing a border, and if it can be made sophisticated enough to know which ones to pick.
As for building and destroying bridges, Dominions isn't about that kind of management. Remember, time in this game passes by in seasons and years. It's not necessary to simulate things that are on such a small time-scale. You can assume that bridge building and destruction happens all the time in the grand scheme of things.
Really what the game needs is a 3 dimensional battle map. Total War does it best. Their maps are divided into 9 squares, with one at the center where the attacked province is. Attackers AND defenders can enter in from multiple sides.
This is easily beyond the scope of Dominions 3, though.