Is it possible to put portable air conditioner outside the house?
There are commercial units designed for this application, there should be no reason you could not convert yours for it.

However, you should consider:


if your unit is rated for indoor use only, you will be voiding the warranty and possible creating a shock/electrocution hazard; use a G.F.C.I. please
UV damage caused by exposure to sunlight, consider a shade structure
restriction of factory vent ports by McGyvering duct work to it may cause sub-optimal performance or may cause damage to the unit
air inlet exposure to outdoor dust and debris could affect the unit