Welcome to Japan. It is not too chilly in Tokyo and Nagoya but it is colder than Indonesia of course, so you had better be with detachable warm clothes (because it is warm in the building.) It is not expected to snow so often. It may sometimes rain so it might be convenient for you to bring a folding type umbrella. However, if your umbrella is expensive, it would be better to purchase in Tokyo because a vinyl umbrella is very cheap. Uniqlo is in sale just now so it might not offer specific bargain in January. I think you can enjoy eating in Nagoya even if you are Muslim. (a little bit strong taste.) I hope you enjoy your travel.