Yes, you can paint it. The more stuff you take off the better the finished job. If it is for one summer I would leave it as is. If it is worth doing, it is worth buying proper marine payment meant for deck use. These require more care than latex house paint but are not beyond a careful amateur's ability. I have used Signature Finish paint that you get direct from a guy in Florida who provides very detailed instructions and all the bits you want. Certainly this is not the only way to go. Check the websites for Interlux and other marine paints.
BTW, if you are going to paint no-skid you want to add a compound to the paint. These range from very coarse to finder. You add it to the first coat and put an extra coat of paint without grit on top.
BTW, if you are going to paint no-skid you want to add a compound to the paint. These range from very coarse to finder. You add it to the first coat and put an extra coat of paint without grit on top.