I think there will be enough pressure. If there isnt just raise the barrels some more. Im generally impressed by how much pressure there is out of a rain barrel.

Raising the barrrels will definitely help to promote more head pressure and perhaps developing a contraption to collect rainwater or melting snow would be beneficial as well.

Here is a link that might be useful: Everything Outdoors USA

FYI- water pressure at level is 14.7 PSI, for every foot above that, add .433 psi. Therefore, If a 3' high barrel full of water is 3' off the ground, the psi at the bottom faucet will be about 18.4 psi. Point of reference, your house psi is usually between 40-60psi. Thats ok, as long as you keep the distance short( reduce friction loss). obviously, as the level goes down, so does the psi.

Sorry, but the last post is a bit misleading . Atmospheric air pressure at sea level is 14.7 psi. The water pressure at the base of a 6 foot water elevation is .433 x 6 =2.60psi guage pressure. If your interested in the absolute pressure, then it would be atmospheric(14.7 at sea level) plus guage( 2.6psi) for a total from this example of 17.3psia. Guage pressure is generally what you would go by to figure your losses in a sprinkler system. If you use absolute values for any of your readings, then all your calc's have to be in absolute values. The end result will be the same either way as long as you stay with the same type values. I would just stick to guage pressures.