That is a hard no-go for any modern diesel, unfortunately. The turbo ice issue seems to be limited to people that park outside and don't have a good catch can. I'm at 94k miles and live where it gets below 0F in the winter but I park in the garage that never gets below freezing and haven't had any issues with the cold.
Those short trips are going to mean the DPF reaches 100% full quickly, the DOC will never gets up to full temp, and if a regen were able to start it would have no chance of ever completing because of those extremely short trips and you'd end up in "keep driving" (DPF > 100% full) or limp mode. If you did a longer (50+km) drive every week then you might be able to avoid short-trip issues with the emissions but it's not guaranteed.
The other problem is those short trips are going to create a LOT of condensation and acid in the oil because the oil will never get up to temp often enough to boil them off which means your oil change interval is also going to be very short due to contaminated oil.
That driving routine is going to be hard on any vehicle, but it's going to be extra hard on a modern diesel with a DPF and SCR. I love my truck, but they're not for everyone for one reason or another. Your use case is the perfect example of pretty much the worst thing you could do to just about any vehicle, but especially a diesel.
Sorry!