Myanmar/Burma is mostly Buddhist, but there are a fair number of Catholics in some cities and a pretty good number in many rural or tribal areas, like Kachin. This photoessay includes a picture of some Catholic ladies in Kachin. They are wearing squares of lace as mini-mantillas. Most missionaries here came from Italy, France, Spain, or Portugal, so they follow the pattern of Southern European customs instead of wearing hats.
A brief history of Catholicism in Myanmar, from the local diocese. In English. There are some amazing stories in a short space: hidden Christians, shipwrecks, beheadings, and incredibly hard work.