>When adding a column to a table, I can't see the new column in the object explorer pane till I exit MSSQL and return.
>The intellisense sees it and I see it in a query, or when I select "Design" from the context menu for the table.
>Is there any way I can refresh the object explorer to show it?

Press F5 to refresh object in OE or right click on the object and hit refresh from the context menu.