I card with a dry piece of denim and don't rinse, the denim pulls off all the rust. I don't use just one piece for a carding because the rust smooths and fills the denim weave, I may use 5 or 6 denim patches for each carding, I use both sides of the patch and swap them out when a patch get dirty. The only time I rinse is when I am neutralizing after the rusting process.
I brown outside in the winter sometimes if the temperature is in the 40s or 50s, as long as it is humid outside and above freezing the temperature doesn't seem to matter.