Leeds Bradford International airport is amongst one of the most challenging in the UK in adverse weather, its altitude means that it is often shrouded in cloud (often referred to as high speed fog) the bigger problem is the runway alignment is not toward prevailing winds, westerly or easterlies and that is down to its history as a departure airport for 2nd world war bombers at the factory (now warehousing) to the North of the airfield.
The runway dips up and down and in places has a cross slope, a combination of strong winds, cross slope can result in standing water, the aquaplaning speed (9 x square root of tyre pressure) would be below the touch down Vref of the event aircraft.
Looking at the pictures it would suggest that the mud all over the left wing could only have occurred due to full reverse thrust until a full stop, full reverse can lead to control difficulties in strong winds.
The Boeing V Airbus debate has some merit, but only in so far that landing weight on a like for like comparison will result in a Vref about 10 knts faster for the 737 because the tail clearance is significantly less on the 737 than the airbus.
The AAIB will confirm pilot experience levels, Tui have moved a lot of pilots onto the 787 and have been heavily recruiting new pilots onto the 737, the sim centres at Gatwick and Burgess Hill have been full of Tui TR courses (and still are) since Xmas
The winds on the day were generally from 070 degrees, given the runway was 14 and they have gone off to the left, then it looks like control difficulty during reverse thrust, hopefully auto brakes MAX had been selected and they didn't cancel it? very difficult to apply max manual and apply rudder inputs at the same time