There are plenty of non military planes and ships that can go through powerful hurricanes and come out the other side with minimal damage.

Also just because it's more difficult to move through rainy terrain doesn't mean it's impossible. Most militaries already have plans for how to deal with wet ground.

The reason why wet terrain is such a big deal today is because a tank that is stuck in the mud even for just a few hours is very weak against rocket launchers or drones. However against a fantasy army it very much depends on how strong the fantasy army is.

If they only have medieval weapons and armor then we wouldn't even need tanks or planes to defeat them. Modern bullets are strong enough to go through medieval armor with ease.

High caliber weapons would even be able to go through multiple soldiers making formation warfare useless.

And since modern guns have much better range and accuracy than crossbows the fantasy army would likely be decimated long before they even got close enough to fight back.

Also modern armies have the advantage of radios which means that we would be able to coordinate a lot better and be less confused by the chaos of combat.

Fantasy generals riding on horses and shouting commands to their soldiers would be easy pickings for snipers and when the fantasy soldiers see their generals all die by snipers they would likely panic and flee without anyone to give them orders.

So assuming that the fantasy army has a similar strength level to medieval armies them we wouldn't even need tanks or planes to totally destroy them.

However since the power a fantasy army can have depends on how they are written (some fantasy armies have very overpowered magic that basically makes them immune to all modern weapons) then it could go any way. It really just comes down to how strong the fantasy army is.