I love the soft sided coolers for paddle raft missions. I used to use a California Designs, but it was not very durable. I now use the NRS Saddle Bag Cooler
and a Frost Pak
The Saddle Bag is durable and holds ice well. Straps around a thwart easily. You do have to remove the Velcro liner and bottom tray after use to let it dry out. Mine has been used and abused and is still in good condition.
The Frost Pak is the BEST soft cooler out. I picked up mine at a "used" sporting goods store, but it still holds ice all day with NO LEAKS. You can use it in a vehicle or bring it in the house and will not have a puddle. Mine also fits in the basket attached to the rack on my 64 Schwinn townie. I strap it to a thwart using 2 4ft straps. I'm tempted to get the 25Qt or 40Qt as well.
I made a chain link fence Top Rail Cooler frame for the boat as well. This makes it really easy to take a full size cooler on a paddle run for day or overnight. We added an umbrella mount (for a Sport Brella) by using some black pipe with 1/2 emt sleeved over the top and a U bolt.