Shortly after buying my house from Carol last December, she and I ceremoniously cut down the aster that winds up the front stoop post. However, this was only after I carried in unknown quantities of aster seed through the front door each time I entered, attached to my coat sleeves and my hair, not to mention the boatloads of seed tracked in on my furniture as the movers hauled it up the front step. Cutting the aster down changed the whole look of the front door, but kept my floors clear of aster seed tumbleweed.
The aster came right back in the spring, as expected. Despite being quite the hardy plant, it struggled this year. Some creature - a deer, I imagine - kept eating it to the ground as it tried to stretch its way up the post. The plant ended up much smaller than last year, and I decided to keep it up through the winter. The tiny seeds end up in the house, yes, and especially on a day like today when the warm winter sun insists that you leave the front door open and take a seat on the front porch to eat soup and bread and cheese, letting the aster seeds float in and take up residence in the corners of the front room as they wish.