Note that it is very important to use carpet where the fibers are woven into (rather than glued onto) the backing. If you can find outdoor or industrial carpeting with this quality, then I'd say go for it (possibly moreso on the outdoor, which is designed for diverse abuse).
I would call the added weight of water to the carpet a non-issue--you might feel an extra ounce or two, but nothing that's going to inconvenience you.
The non-slip qualities of carpet really are superior to felt. I noticed the difference as soon as I stepped into the water. Don't go ripping good felt off of your intact wading shoes, but keep this in mind once it wears down.

Andrew