As far as I know there's no specific advantage to using a linear polarizer so for safety just use a circular polarizer.
The difference between the two types is not what the names suggest.
The linear polarizer has polarized light as it's output. The circular polarized has another layer that scrambles the light so that what comes out of the filter is not polarized.
You pay more for a circular polarized but you know it'll not mess up anything in any camera. The only thing you cannot use circular polarizers for is the trick of using two polarizers to make a variable ND filter but that is of no concern in your application.
I have also heard that the whole linear/circular auto focus thing is a myth.
Video cameras auto focus fine with both - so i was told.
Personally, i had bought CPLs before i knew about this. So never had the problem.
What do others think? Any evidence to prove otherwise?
"i usually use a cpl in my matte box for shooting horses, would i see any difference if i used a linear"
Visually there should be no difference, the whole "auto" thing I haven't a clue.
To my mind apart from a being a bit more expesnive there's no reason not to use a CPL so I would suggest playing safe. It's a bit like always using balanced audio :)