My concern with a tri-fold was in winter if any ice/snow was on the tonneau it may damage it.
I live in the great white north and have never had any problems with snow or ice on my Extang cover. It even stays flexible to fold up in extreme cold. Occassionally the edge seals will freeze to the truck rails but pull loose pretty easily. The nice thing with the soft cover is that the snow breaks loose and comes off easy when it flexes.
Only real downside is the cover material can flap against the cross rails at speed. A little annoying noise wise if you like to ride with the windows down.