unexpected arrivals

I don't have flower beds so I plant flowers in pots and hanging baskets.  Nasturtium leaves have started appearing in different places around the perimeter rocks in the garden, and I'd love it if they would survive the winter, but these leaves are showing signs that they won't.  I've always thought of them as annuals, but I googled to find out if nasturtiums are perennials, and the Farmer's Almanac said that they may act as perennials.  I'll be watching next spring to see if they appear.  Nasturtiums are one of my favourite flowers and I'd love it if they would reseed themselves in unexpected places, like the little violets have.