There are recommended temperatures for serving wine. White, Rosé, and Sparkling wines are intended to be served chilled and Red wines are intended to be served closer to room temperature. Keep in mind that these are guidelines and you should enjoy wine at whatever temperature you like.
For light dry white wine, white dessert wines, rosé, and sparkling wines the recommended serving temperature is 40°-50°F. This is a little warmer than fridge temperature which is usually about 36°F. This means that you should chill these wines in the fridge and then once they are at fridge temperature pull them out of the fridge about 30 minutes before serving to allow them to come up to the recommended serving temperature. The reason to serve these wines chilled is to preserve their fruity freshness. With sparkling wine it also helps to reduce gushing when opening the bottle and when filling a glass.
For full bodied white and light fruity red wines the recommended serving temperature is a little warmer. Here you want to target 50°-60°F. This will help preserve the fresh and fruitiness of the red, and with the white it will allow you to pick up more of the aromas. With these wines you would want to chill the wine in the fridge for at least an hour before serving, or if it is at fridge temperature then pull it out an hour before you plan to serve it.
For red wines and ports the recommended serving temperature is between 60°-65°F. This will make the tannins in the wines seem less astringent, and also reduce the perception of bitterness. These wines should be put in the fridge for about 30 minutes before serving them. Most people, and restaurants serve red wines at room temperature which depending on where you are is in the range of 72°-75°F degrees.
Can you put ice cubes in your wine? Of course you can, it is your wine, and you should have it the way you like it. I do not recommend ice cubes only because they will melt and dilute the wine. Maybe look into some of those whiskey stones that you put in the freezer and then use to keep your drink cold without melting.
Those sounded a lot like rules, but they are guidelines. In truth you should serve the wine at the temperature that you like it best. If you like your sparkling wine right out of the fridge then have it that way. I like it too. If you are used to room temperature reds then go ahead. At warmer temperatures you do smell and taste more of the aromas in wines. If you like chilled reds, you do you. The best temperature to serve a wine is the temperature at which you enjoy that wine the most.