Why does the outside temperature feel cooler when the humidity is low as opposed to average or higher humidity levels?
I would suggest that the opposite is true, you feel colder with the increases of humidity at cold temps. Water(moisture) is a better conductor of heat then air, therefore it removes heat from your body more then air. The actual feel you may be speaking of is possibly how it feels on your lungs and mucosal membranes? In dry cold weather this can cause irritation.
In warm climates, high humidity makes you feel hotter. This is because the body's response to heat is to sweat: sweating allows evaporative cooling, through the latent heat of evaporation getting put into the water and therefore being transferred from your body. When the humidity is high, there is little room for water to move into the atmosphere (it only does so until the humidity is 100%). Thus you don't get the cooling effect that you would in dry conditions, so it feels hotter.