A "mixer" is just some way of (semi-)randomly pairing people up to dance for a short time, not even a full song, just a short part of one. This can be done in various ways including lines pairing up one couple at a time or circles pairing up everyone at once. In a line-type one you'd typically keep the music playing all the time, dance down the floor, get back in line, and repeat. For a circle-type one, you need some signal to tell people when to stop dancing and circle up again for a new partner. That could be done by stopping the music or using a whistle or something. I'm sure there are names for at least some types of mixers, but I don't know what they all are. A "foxtrot mixer" would just be a mixer where the dance used for it is a foxtrot instead of say a waltz.
Personally I don't like mixers. I'll ask people when I want to ask them and I'll accept requests from any woman who asks assuming I know the dance. I don't need mixers forcing me to dance with people. They can be good, but I don't like them.
If you're going to do them though, I think it's generally better if you do it in such a way that most of the people can be dancing at the same time. The circle style pairings are great for that since everyone gets a partner at the same time. OK, an uneven male:female ratio throws things off, but the people who miss a cycle will probably get someone on the next partner change, so it's not too big of a deal. The linear ones aren't quite as good because you still have a large fraction of the dancers standing in line waiting for their turn. The snowball can be even worse in a sense. That's where one or two couples start dancing for a bit, then they're told to get a new partner which doubles the number of people on the floor. (The number of dancers grows and grows just like a rolling snowball increases in size, hence the name.) Repeat until everyone's dancing. Ghostdancer seems to have a different definition of a snowball, but this is the one I've always heard. The problem with this is that some people may not get picked until the end for whatever reason and end up sitting out nearly the entire mixer. For those people, that kind of defeats the purpose of having a mixer.
Just a few thoughts on the subject.
--
James Marshall
marshall@astro.umd.edu
http://www.astro.umd.edu/~marshall