I should be more worried about the wind resistance that the boards will present. You can support quite a lot of weight on relatively spindly posts with the right fixings in still conditions - indoors for instance. These boards are exactly what you will see erected as hoardings around construction sites - have a look at the posts used on those. A full size solid board will require a substantial post not to snap in a strong wind. Edit: Just read your earlier post more thoroughly. If it is a double sided strongly made fence I wouldn't worry about the weight of the boards once fixed.
Louise (double-checks spelling), how large will these panels be? And what type of fence is it going on - is it closed-boarded, for instance? If so, then wind resistance ain't an issue as it already has that aplenty. Weight is also extremely unlikely to be an issue - provided you do attach them to the actual posts and not to the fence panels. If these mural boards are significantly smaller that the fencepost spacings (usually 6'), then you generally have two options - if the panels are 'small' (say up to 2 or 3 feet wide) then then can be attached to a single post and 'should' be fine (unless vandalised), tho' they might benefit from having strengthening rails attached to the their backs. But if the m-boards are, say, 4 or 5 feet wide, then you will likely need to have a couple of horizontal rails spanning a couple of posts and screwed securely to them, and the mural boards then screw to these. Make sense?