Do energy codes permit mechanical cooling for exterior spaces?

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I do not see any provisions in 90.1-2010 (or 90.1-2013) that prohibit the use of mechanical cooling for exterior spaces. The closest requirement that I know of is Section 6.5.8.1 Heating Unenclosed Spaces which requires the use of radiant heating for spaces that are not enclosed. So at least you cannot blow heated air outside. The lack of a cooling requirement is unfortunate in my opinion.

Another section in 90.1-2013 (not 90.1-2010) is 6.5.10 Door Switches which either disables mechanical heating and cooling or requires a huge setup (90F) and setback (55F) when a door is open to the outdoors for more than a few minutes. Still not exactly what you want but it does imply an intention, perhaps, of how the outdoors should be treated.

Please note that this is my personal opinion and interpretation of the standard and should not be considered an official interpretation (I say this because I am a member of the 90.1 committee).