Looking at the photos at this site, it appears that they are able to be installed horizontally.
Do you have to use a track or can you drill into the shutters and then Tapcon them to the masonry? I am thinking of using 2 inch L x 1/4 wide Tapcon for this application.
For my application, there is a sill that protrudes out underneath my windows, which prevents me from placing the shutters vertical in a track. The protrusion looks something like this (see brick under window):