Steve is right, carpet does get old and rip and stain and hold a slight stench at times. However, if you fish in the winter you want carpet or something to keep your deck from getting slick. I have carpet, I have friends that don't, I dont worry about slipping, they do, I have to glue my carpet down sometimes, they dont.
Bottom line, if you dont fish in the winter then dont have to worry about ice go with no carpet. If you fish all year around no matter the temps, put carpet down. One thing to think about is the sound and things hitting your deck while you fishing.
Icthus