leave the painting till summer. If you stuff it with p38 and rust killer etc you need to have a damp free few weeks. If and when its dry enough get it to bare metal, treat it then get a near colour match rattle can and spray it on untill you can get it to the body shop.
Putting primer on is no good its porous and in this weather will just be a waste of time.
If you want to do it yourself then dont foget that body panels mainly rust from inside out (unless its just a stone chip) treat the problem to find the cure eg when dry (nice long summer) scrap all the old underseal off from the inner sections and drown the little begger in waxoil, only do this when the old underseal is dry and crispy. then you have a good base to work from and you`ll get no bubbling from the new paint come winter. When doing anything like this drive the car onto a big plaggie sheet so when you`ve finished covering yourself in *Bleep* and waxoil, drive the car off, fold and take down the tip. Happy car, clean drive (in seconds) = happy wife