Nope, no explanation either for Comet's super-intelligence or Brisco's ability to understand Horse.

It does occur to me that Brisco isn't the only character who talks to Comet. Bowler and Prof. Wickwire both interact with Comet on occasion; I'm not sure Bowler understands Comet's "dialogue", but I think Prof. Wickwire very well might.

It's really a pity the series didn't last another season or two; had it gone longer, I strongly suspect we'd eventually have gotten an episode in which Comet fell in love and we got horse-romance in our horse opera.