Do you think the water is getting drawn though the engine? as in through the intake? because that's the only way the water would get into the exhaust
The exhaust has a hole at the tail end. Water molecules are smaller than the hole.
Water drawn into the engine intake will do one of several things, dependent on quantity, relative to the airflow at the time.
A small amount may atomise, and turn to superheated steam during combustion, the expansion of which will give a power boost. Engineers have been experimenting with water injection for many years, not perfected yet. You may feel your car seems more powerful on a day with high humidity, and it will be, for this reason. The good mix of water in the air is great, but to do this in a controlled way requires a mixing airbox as big as your house.
A little more water, instead of atomising and creating steam, will instead cool the intake mixture, and the burn temperature, reducing power, but will still pass into the exhaust as water vapour. A little more still, may just put the fire out, causing misfires and unburnt fuel to pass into the exhaust. Bad news for a hot catalyst. The already hot exhaust will still turn in to vapour.
Add more water, and it will hydrolock, breaking pistons, bending conrods, and often destroying the block.
None of the above will cause a gurgle in the exhaust.
As the exhaust valve opens, the gases rush out of the cylinder. As the valve shuts, the gases are still moving, creating a depression behind them. This causes the gas to effectively do a two steps forward, one back, which is why at the tailpipe we can feel the pulsing. That pulsing will draw in water, but often fail to push it back out again. Don't know why, there is a physics explanation, not memorised. This is why when driving through floods, it is important to use a low gear and higher revs, to discourage the water flowing all the ay up the pipe. If an engine is left to tickover, with the tailpipe under water, it will draw water in, including up into the manifold, and into cylinders. Difficult to get one's head around, but it does happen. Great fun proving this at college, (1972/3), with an engine on a rig in the test workshop. Modern engines are more fragile, and probably not good for such an experiment. Vehicles that are set up for temporary wading will have snorkels on the intake, leaving the exhaust normal. Those used for longer periods in water will often have snorkels on the exhaust too.
So a big enough puddle can cause some to be drawn into the exhaust, where the heat at the tail end is lower, especially on a colder day, so it will sit as a puddle, and gurgle, taking its time to boil off.