You just can't be barefoot.
There is a footrail along the inside of the boat, in front of the seats. If you keep your feet on that, you will be able to keep your feet pretty dry - unless you are in the seat that gets water dumped on you. But, even then, if you keep your feet on the rail they will get a lot less wet.
Looks like Muffy was posting while I was typing. When we rode with our whole family a few years ago, my mom got completely soaked - except her feet, which she kept up on the rail. The only one in our party who got more than splashes on their shoes was my youngest DD, who is disabled and was not able to keep her feet on the rail.