There are a couple of things you might check.
First off, there is a cold air intake, which personally, I think is a real problem. It goes from the engine compartment to the top of the left wheel fender. If your wheel fender skirt is missing, or if you have a break, especially toward the back of the fender skirt, it will direct water directly into the cold air intake.
As an additional warning, NEVER drive into water that is deep enough to splash over the front fender. We have seen engines hydro-lock from the water thrown up into the air intake.
There is also a vent at the bottom of the air cleaner that can become clogged. Be sure it drains correctly.
The last element that can cause you this problem is the 'snow screen'. Personally, I think in most cases, the snow screen is actually a bug trap that gets clogged up with bug debris.
It's a bit of a bother to remove all the items to get the whole air intake off and checked, but in your case, make sure you do not have a broken fender skirt or a skirt that is missing screws that should keep water from running directly into your air intake.
Remove the battery box, the air cleaner, noting there is a vacuum hose connecting to it. The fender skirt, if removed or ill-fitting should be re-installed correctly with all the screws needed.
If you read a MAF code, and it's a VAG-COM cable, you can read in a section the value requested and actual MAF reading. The MAF is subject to failure and will cause the engine to go into a 'limp' mode. Particularly, if you turn the engine off then back on and the limp mode goes away, it is very likely your MAF. We do carry all the replacement parts, if you need that MAF.