I found a natural linen riding habit trimmed with green silk om the 18c woman list. There were no pictures, but I'm using it as the basis for my natural linen and blue silk riding habit that I hope to have for UTR.
I also found a white linen/cotton riding habit in the V&A. No pictures though.
I'm also going on in Williamsburg they have records of using lighter fabrics because of the heat.
I have links to the above habits in my LJ under the 18c habit tag. I'm on my phone or I'd get them for you :)