Welding steel, even galvanized to stainless steel is not a difficult task. The most common electrode used is the 309L series, whether it be E309L-XX, or ER309L, depending on your process. The reason it shouldn't be any harder to weld galvanize steel than uncoated steel is that you should remove the zinc coating before welding. There have been several strings in varius forums in this BBS that you can visit about removing galvanizing and the problems with welding over it. It won't be any more of a corrosion issue to remove the galvanizing before welidng, as the welding will remove it anyway. Removing it before welding just eliminates welding and breathing problems. When you are done, just touch up the door frame with "Cold Galv" paint, or use the "Hot stick" method in which a zinc alloy is basically soldered to the door frame.

Good luck with you endeavor,
G Roberts