If, as you drink your cocktail, the large ice gets exposed to the air. Then what happens is that the big ice starts cooling the atmosphere instead of your drink and you get additional dilution with no added chilling. It can be easier for small ice to rearrange and stay submerged in a drink as you sip it. So in the case of a chilled Old-Fashioned, all that really matters is you use ice that stays submerged for as long as you intend to drink the cocktail.
No—you also have to consider water that is on the surface of the ice before you add it to your drink. Small ice has tons of surface area. As a result, it accumulates surface water—liquid water that builds up on the outside of the ice through melting and through condensation. When you add small ice to a drink, that surface water immediately dilutes the drink without adding any chilling benefit.
Of course, this is really much more of an issue if you are in a bar situation where ice is stored at room temperature. If you use lots of small ice directly from the freezer, surface liquid should be insignificant.