Possible to hide columns in a SQL Server Management Studio database diagram?

Unfortunately, no.

You can show or hide whole tables only. Or resize. or reverse engineer into Visio or some such tool

Edit, Dec 2017

"Table View" in diagrams show all columns or no columns. It does not remove some columns

Yes, you can modify the view of column attributes but OP did not ask this.

Read the question please

Actually you can. Just right click on the table and select the "Table View" from the context menu.