Is it possible for two stars to be in a horseshoe orbit around a much larger star? I was reading about how Saturn has two moons, Janus and Epimetheus, that swap orbits once every four years. Could something like this happen on a much larger scale, but with stars instead of a planet and moons? Let's say you had a large, massive star with two red dwarfs orbiting around it. Could those two red dwarf stars fall into a horseshoe orbit, regularly swapping orbits every few years or so?

more about horseshoe orbits
Yes, it is possible, however such orbits are likely to be unstable.

For example in the paper


  Ćuk, Matija, Douglas P. Hamilton, and Matthew J. Holman. Long-term stability of horseshoe orbits. Monthly Notices of the Royal Astronomical Society 426.4 (2012): 3051-3056. doi:10.1111/j.1365-2966.2012.21964.x


it was found that if the mass of second body becomes larger than 1/1200 of the first body, horseshoe orbits become unstable. (Third body was assumed to have negligible mass).

Nonzero mass of the third body was investigated recently in a thesis:


  Balaji, Bhaskaran. Mass ratios in stellar triple systems that admit horseshoe orbits. Diss. Massachusetts Institute of Technology, 2016. abstract, pdf


and it was found that in addition to constraint of Ćuk et al. nonzero mass of the third body  further decreases stability of such systems, so that the lifetime of horseshoe orbit $\tau \propto m_3^{-1}$.

For stars only coupling of more massive giants with lighter  red dwarfs would fulfill  first constraint and then the third star would never have 'negligible' mass, one could conclude that horseshoe orbits when all three bodies are stars are always unstable. And for larger masses of smaller stars the lifetime of such orbits would be too short to expect such orbits in our vicinity.

However it would probably be possible to have stable horseshoe orbits of two stars (say a blue giant and red dwarf) and a planet.