Begin by lightly scrubbing the limes, then rinse them and pat them dry.
Cut off the ends of the limes and slice them into quarters, discarding the white veiny interior.
Place the lime quarters into a blender, add the cold water, and blend until the mixture is mostly smooth, which should take about 1 minute.
Strain the blended mixture through a fine-mesh sieve to remove the pulp and set the juice aside.
Clean the blender, then return the lime juice to it.
Add the ice and sweetened condensed milk to the blender, and blend until you achieve your desired consistency, which should take about 1 minute.
Pour the lemonade into glasses and garnish each with lime wheels.