Given our experience, I might suggest taking some extra precautions when flying into TXL in the winter.
Well, I fly into TXL twice or three times a week and never experienced any problems. When your plane finds itself at a passenger bridge a luggage takes a 30 meter journey at the utmost, half of this undercover.
Certainly the airline is responsible for your luggage, but it will be a bit difficult for you to make your case because you did not report it at the airport. There are plenty of possible reasons why your shirts got soaked after leaving the airport and most of them are not only theoretical....