Some Corvettes have a duct under the front that takes air from very low into the radiator. One of the recurring problems with these cars is the dirt and debris that clogs the radiators.
Not a debiliting issue, but one that does seem like a design flaw.
I think there is a lot of difference between hanging a cooler somewhere in the breeze and locating it where moisture and dirt coming off the tires will be a constant thing.
In an area where roads are salted in winter it may be an even bigger problem. Around here I've seen cars with caked mud/dirt in the wheel wells and I can just imagine that muck completely covering the cooler rendering it useless.