For aqua regia, hot strong acid dissolves silver chloride, cold diluted doesn't and then you can filter it off.
For sulfuric cell (deplating), if the temperature gets too hot it starts to dissolve base metals instead of the gold. In this case ice isn't added to the acid as dilute acid also stops the cell from working.
I would never use ice to dilute sulfuric acid, I would pour acid into water instead to be safe.
Göran