How you hold a wine glass matters if you want to experience the wine's flavors to their fullest extent according to Maximilian Riedel, CEO of Riedel — The Wine Glass Company.
With a stemmed wine glass, Riedel says, "Clasp the stem between your thumb, pointer, and middle finger. You will then use your ring finger to hold the glass under the base."
Holding your glass this way makes it easier to swirl the wine without it splashing out and allows for the least possible contact between your hand and the glass's bowl.
As Riedel says, "Holding the bowl of the glass can, over time, warm the wine in the glass." This may shift the spirit into a temperature zone where its best traits aren't apparent.
Common wine wisdom tends to prefer stemmed glasses for this reason, but stemless glasses don't necessarily kill the temperature of wine if you're mindful of your hand positioning.