I would agree staying on the ice would be the first choice.
Sometimes there are other factors that play into the decision of where to have a weigh in.
Sponsors would be the first one that comes to mind.
Most open water tourney’s are set up to go to a selected location…back to a bar or well, if I recall one tourney goes to a Wallmart.
One new tourny came up with a 2010 idea to have the fish photoed and measured in the anglers boat then released.
This type of tourny isn’t the best for the sponsor (in some eyes) but it’s better for the fish…assuming were talking about catch and release and not a kill tourny.
I would guess this is the same for ice contests.