That's a good question since we do not want to run that antifreeze into the filter, and if you don't the filter will freeze and burst. On my last MH there was a shut off valve leading to the filter, so before winterizing I would turn the water flow to it off, winterize, then remove the filter and drain it manually. The line from filter to sink will drain itself when you remove the filter.
If you don't have a shut off, you can drain your system down, remove the filter and either add a shut off, or take the filter with you to the plumbing section and put together a short "jumper" of tubing with fittings to match those on the filter. Then put the jumper in place on the MH and winterize away.
2016 R-Pod 176T
2002 Avalanche Z71 Tow Veh