I don't think alfalfa would work very well in reseeding as you describe.  Clover - as you mention - is not a good choice for horses.

Frankly, I'd take a  hard look at the grass stand you have.  IF you have bare/this spots, I would look at overseeding more grass into the stand.  And I think you would have better result if you find a no-till drill to seed grass.  Otherwise, I would just fertilize the stand, and take what you get.  Manage it the best you can. A few posts down, there is a thread about Crossbow vs Cimmarron.  Frankly, I would keep the field in grass, and spray with 2,4-D and Cimmaron to help with weed control.  Make sure you understand crop rotation restrictions when using Cimmarron.  It is not a problem to make and selling hay - but it does limit your options to rotate crops in the near future.  

If you really want alfalfa, I would kill the stand down and start over.