I also have an 03 but have not experienced this scenario.
However, I did experience it quite often with a Ford Ranger I used to
own so perhaps the explanation is the same. On the Ranger when taking
Right turns in deep puddles (not as deep as you described) there was a
gap in the wheel well that allowed water to spray all over the steering
pump belt. All that water caused the belt to slip so the pump
momentarilly stops working giving that manual turning feeling. All
would be fine after a moment or two when the belt got some grip on the
Since I never had this in my Santa Fe nor have I heard of it over at
the santafeforum.net I would check inside each of the front wheel wells
to be sure the plastic linings are still in place to keep water away
from the steering pump and belts.
Hope this helps