Let’s get something straight right off the bat- 99% of red wines are not meant to be served cold. With that out of the way- yes, some lighter-bodied fruity reds such as inexpensive Beaujolais or sparkling reds like a Lambrusco show well when chilled.

Something to remember, though- a refrigerator doesn’t just make wine cold- it can also simply make it cool. 

Wine drinkers in much of the world have cool wine cellars to store wine, but many do not. A glass of red wine from a bottle that has been sitting in an overheated city apartment can taste of fruit and alcohol and not much else.

Putting that bottle into the refrigerator for two hours will make it too cold- but putting it in for, perhaps 45 minutes, can take the warmth out of the bottle and bring the wine down towards cellar temperature. Which is awesome.

There is a lot of static about serving temperature of reds. Keep it simple- 60 degrees F is a good target if you have a wine thermometer.

Otherwise, just put it 'in the ‘fridge for 45' minutes. You’ll find the aromas and flavors are more noticeable, alcohol is muted and the initial sensation is more pleasant. 

Of course, if you have any sort of wine cellar you’re already in good shape. With a bit of experience, you’ll figure out how long to let the bottle sit at table before opening.