The easy and most accurate answer is to get rid of the carpet... I know, it looks nice, and it doesn't get as hot... etc. but fact is... where their is damp carpet... their is mildew - and I would bet money that what you think is "moss" is actually mildew - as it can certainly look like moss.
There are pontoon flooring options and alternatives to carpet... Vinyl is probably your best; but, if indeed you want to keep your carpet, then I would suggest a small power washer.
I know from experience that if you roll it up and take it off - (as the other person suggested) you will not only find that to be a pain in the you know what... you will actually have a worse problem when you unroll the carpet again. You will only do that once, and you will never use that carpet again.
Years ago, I invested in a small Sears powerwasher. If I remember correctly it was just short of a $200 investment... and it was one of the best things I ever did for my boat...
I tell you... I clean everthing with it - from my upper helmstation to the bottom of my hull (yes, even while it is in the water).
I loaned it out a few times to boat neighbors in my marina, and most of them have since purchased their own. I use mine about 6 times a year on a regular basis, and maybe two or three again when something comes up and I really want my vessel to look "ship shape".
Course, this is not a prevention for mildew (only clean & dry is that... and you won't find that on a boat; but it sure does a quick and easy job of getting it all off...

Happy & Safe Boating!