Mine only wear clothes outside, when it is cold.
Young puppies can get chilled very quickly, although as it is technically summer (LOL) you shouldn't need to dress your puppy.
Chihuahuas like to snuggle under blankets, so as long as he has plenty of bedding he should be fine. Mine also had covered beds when they were little (cat igloos) and each other for warmth.
You will probably need a coat of some sort for winter, but TBH it was so mild last winter that mine hardly wore theirs. They don't stay still long enough to get cold.