A euphemism for engaging in sexual escapades with a female of dubious moral character. Just as with a real life swamp, if you don't wear some form of protection, there's no telling what sort of diseases you might catch.
Leliana: "She was...you are...you're giving her...I mean, you're wading through her swamp!"
Warden: "Are you jealous? I could wade through yours if you'd like"