Dawn and dusk are the times during the day mosquitoes are out the worst. It is also the best time to spray with deet to protect from getting west nile. It works by not allowing mosquitoes to zero in on a source of carbon dioxide, which is how they often find their victims. There is a comparative association between the amount of deet in a product and the duration of protection.
Dawn and dusk are the worst times of day, deet will keep them away, but if you are bitten at all there is a risk, all be it low that you could contract west nile. Try to stay away from ponds or water sources at those times wear longer clothes when out at these hours, and yes wear deet.