Wait until Spring and then cut it all out and weld in fresh metal. I will tell you this: The rust will most likely be worse than you imagine once you dig into it. Once you cut the outer rocker skin off, the inner typically is in varying degrees of bad too. I had these problems on my 02 GC and i live in Delaware where we hardly ever get snow and I just cut out and replaced 85% of my lower inner and outer rockers. It is a bad design that we all have to live with. Good luck!
2003 Rubicon - 33x12.50x15 GY Duratracs, 15x10 MT Classic Locks, 2" BL, 2" BB, Warn Front Bumper, Garvin ATS Rear Bumper, Body Armor Extreme Rock Rails, Nth Degree Tummy Tucker, Skid Row Engine, LCA and Gas Tank Skid Plates, Teraflex Quick Disco's, Uniden Pro 520xl CB, 3' Firestik Antenna, BW Flat Fender Flares, Tom Woods DS, Currie Rear Adj Arms