I waited about five minutes for my bus. In that time, I saw other women, in ones and twos and threes with the occasional man, walking towards the funeral home, and all of them pulled scarves from their purses or picked them up from around their necks and tied them under their chins - sometimes fighting the wind on this lovely, bright, hot day - before going in. Mostly, they wore skirts, and the tops were appropriate for the weather (unlike my own long-sleeved blouse), but it was apparent even from half a block away where they were headed.
It was something I've actually never seen before in all my years of waiting at this bus stop - I've seen funerals, of course (although 9:30 is a bit early), but not the ladies of all ages tying on babushkas. (Although Wikipedia tells me that Russians ever actually use the word "babushka" to refer to the scarf.)