I'm not clear about where you see the drips of anti-freeze. Is it coming out of the supply line where the filter connects or out of the filter itself? With the supply line not connected yet, turn on the water pump and flush all anti-freeze out of the line into a bucket. When running clear, install a new filter (or the old one if not full of anti-freeze) and connect to the fridge. For next year's winterization, I'd install a shut off valve right before the filter. This would allow the removal of the filter and flushing the line to the filter and then shutting that valve down while the rest of the plumbing gets anti-freeze pushed through it. The small quantity of water in the ice tray can be sponged out, evaporation will take care of the rest.
If you see anti-freeze in the supply line between the filter and the ice tray, use a short piece of hose to connect in place of the filter, run water all the way into the ice cube tray and cycle it a few times.
Bob & Donna
'98 Gulf Stream Sun Voyager DP being pushed by a '00 Beetle TDI