Dave is quite right in that the project is entirely implausible but it is possible to get decent COPs out of Peltiers. For a delta T of 8C the COP can exceed 5 which means the panel would only need to be 50W (still huge). To get that COP you'd have to run Peltiers at around 10 to 12% of their peak voltage, and 50mm square devices would only pump around 20 to 30W each at most (perhaps 5% of Qmax). Thus you'd need at least 10 of them but they are pretty cheap on Ebay. They would weigh around 250g in total so not too bad.
Delta T of 8C isn't much so you would need some decent heatsinks, but having lots of Peltiers helps considerably by increasing the area through which the 300W (@ COP = 5) of heat has to flow and thus the temperature differences required at the Peltier/heatsink interfaces. Using the cooled, dehumidified air to cool the heatsink would also help a bit. Still 300W, Delta T = 8 means heatsinks with less than .027C/Wwith moving air. How fast can you peddle?
Drop Delta T to 4C and COP could in theory exceed 7 or 8 and you would need less of them as they could transfer over 40W apiece at the lower delta T. The heatsinking problem would get more difficult but not impossible - it would probably only need a few hundred kilos or so of aluminium or copper...
Perhaps one of the most difficult problems would be managing the airflow so it spends just long enough on the cold side to release sufficient of its water but not getting cooled below the dew point any more than necessary wasting energy. If it flows too quickly though energy is wasting by sensible cooling of the air + water vapour, but not enough to condense any or all of its water. Quite tricky I'd have thought as you would need to be able to measure RH fairly accurately.
Might be more sensible to carry a few bottles of water and flog them to your cycling buddies examining their few drops of tepid, polluted condensate (distilled eau d'cyclist sweat anyone?) after a few hours of cycling in 40C/90%RH conditions.