There is a charming video on the entire process from weaving to finished hanten at a factory in Japan, and it is kind of worth watching to get a solid idea of the construction process. This other video shows a smaller production establishment, but as you can see, they are using a very specific kind of fluffy cotton wadding that, I suspect, is not easy to get outside Asia.
Here is a Japanese pattern for a Hanten, translated into English.
I have made a PDF of this for convenience you can download here, but the credit for this handy translation goes to Yifarn at Japanese Sewing Books.
Folkwear.com has a pattern for a hanten, although it calls it a ‘padded jacket’ and it comes as part of a package they offer in either paper or pdf form called Japanese Field Clothing. This includes a pattern for a hanten, a hippari and mompei pants.
They also have a long, detailed video on how they go about sewing it. However, I did find this method of construction quite disorienting, perhaps because I have learned to construct in a Japanese manner, and this is a more western approach. But if your experience is primarily with western garments, this step by step video might be of excellent use. At the end of the day, you want the finished garment and however you decide to get there is fine.