Why would hot water pipes be smaller than cold water pipes?
Hot water delivery times are highly dependent on the size of the pipe. It will take more than twice as long for hot water to reach the fixture travelling through a 1/2" pipe than a 3/8" pipe (because there is roughly twice as much cold water sitting in the pipe), and more than twice as long through a 3/4" pipe compared to a 1/2" pipe. Thus, using the smallest supply lines possible for hot water plumbing to fixtures will supply hot water much faster, saving water and energy, and making occupants happy.

With cold water supply lines, there's no similar issue. Instead, our only concerns are about supplying enough water for good flow rates, and stable pressure (so output doesn't noticeably fluctuate when someone flushes a toilet, for example). So for the same fixture where a 3/8" hot water supply line makes sense, it also makes sense to use a 1/2" cold water supply line.