I have found a way to hide a column in the matrix visualisation in Power BI but not in Paginated report, hence question.
In the Design view, you can hide a column by right clicking the column header and selecting Column Visibility...
then select Show, Hide, or based on an expression
To tie showing or hiding the column based on a drop down, create a parameter by right clicking Parameters in the Report Data pane and selecting Add Parameter...
Here are my settings for the parameter:
Once you have the parameter set, go back into the Column Visibility settings, select based on an expression and click the fx button:
Then click Parameters and double click your parameter name to add the expression:
When you run the report, you'll see the drop down and the default setting:
You can then change the drop down and click View Report to see the hidden column: