Do children belong at a wedding?

The question of the day (or perhaps of the week) is whether or not to have kids at our wedding.

Michael's brother's kids are one thing. They come with the package. Anyway, the eldest is very well behaved and the youngest is too young to make trouble. No, my concern is with other people's kids.

We have, I think, three guests (or couples) that have children - nine children total, between the three of them. Because we are trying to keep the wedding small - and, actually, because the wedding is going to be at a winery - we're thinking of excluding the children. But, how do we go about asking this of our guests? A note in the invitation? Ask them in person? I have absolutely no idea how to handle this.

If anyone has any ideas of how to handle this - either from personal experience or common sense that I somehow don't have - please feel free to comment or contact me. I would love to hear your input!