I have not found the 'fan with a tank' type coolers to be very effective. I have run one off battery via inverter as they only take present about the same load as a furnace. They do circulate the air and, at the Salem I'Rally, did help by doing that. I figure the cooler helped inside temps by maybe 4 or 5 degrees.
Rich has one of the 12v
roof types and is quite happy with it in the Eastern Sierra forests (he is a wilderness steward for the NFS). Water from a creek and powered by a portable solar panel. ($600 cooler and $600 solar last I checked prices)
Figure that you are going to need about a gallon of water per hour and 50 watts or more electrical for a swamp cooler. The electrical is continuous as a contrast to the furnace cycling so its impact on battery power is more severe. Of course, it is most needed when the sun is doing its thing so a 100 watt Solar panel could keep it going. maybe.
The mobile home type swamp coolers use third or half horse blower motors plus the water pump (500+ watts) and can run through several thousand gallons of water per month. They can provide excellent cooling for 5,000 cubic feet as in a typical single wide. (an Airstream is a bit under 1500
cubic feet with less insulation and larger surface to the volume for comparison)