Well yes.. ice make a difference ....
A few years ago a wonderful small plate/tasting/tapas craft cocktails place opened within walking distance of my house... an amazing little restaurant..
The S/O and I prefer to sit at the bar, rather than a table...we watch the barkeep...mix, muddle, shake, she makes her own extracts and bitters..
And she spends a lot of time shaping ice..
She explains that the different shapes.. have different surface areas, hence different rates of cooling and dilution..
She usually puts a crystal clear cube or sphere in an Old Fashioned...
Cocktails
If you ever happen to be in my town, run, don't walk to have a meal at this place