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.
fashion statements. Some clothes are needed. My short haired chi's shiver at anything lower then 70f so t shirts are a must on colder nights or when my air conditioner is on full blast. but my sister long haired chi doesnt get start shivering into the 60f . In the winter your going to need something to put on your chi if you ever want him to pee outside during the cold months. they are tiny and get cold easily. mine will still snuggle in blankets and its hot outside. but your getting a puppy chi and not much is going to fit him at this point unless hes over 2lb you cant find much. Chi's only really shiver when they are scared, excited or cold
Toby has some coat for winter and t- shirts for everyday wear. He gets cold when the air is on and since it has been 100 degrees f it's been on full blast. I'll usually let him wear a tee whenever he wants it. He will tell me when he wants it by dragging it to me. Clothes are food to have with short coats, even I'd by for a fashion statement and only for practical reasons.
Odie has a small wardrobe, but everything is well used. We live in a semi-arid area, and it gets pretty hot in the summer and we keep the air conditioning pumping. We keep our place too cold for Ode sometimes, so she's been known to wear a sweater or two indoors during the summer (only when we're home). I think at least one sweater and one jacket is a great investment.