Well, you could probably get away with doing that. If you want to completely decompile an apk, use apktool:
[UTIL][03.09.10] Apktool v1.3.2 - a tool for reengineering apk files - xda-developers
Just install it, and run it from the command line. It will give you the options for how to use it. I've done the same sort of thing you're asking about with launcher pro. It works fine. I did, however, use apktool to completely decompile it. If the images are available by just opening the apk, you could probably do it without it. Try it and see what happens. This is an apk, so as you said, you must sign it. It will never install if you don't. it's not an option like it is with flashable recovery zips. Also, you can sign apks on the fly from your phone with signapktic. It's in the market, I believe.
All that being said, you might be thinking to far into this. While you'll need to do the above for most apps, a lot of weather apps just use some sort of skins. Beautiful widgets, for example, stores all it's skins on the sdcard. You can just open the directory for whatever skin you want to modify, and replace the appropriate png with whatever you want (assuming you keep the png sizes the same). It's ridiculously easy, and doesn't require messing around with the apk at all. What weather app did you have in mind?
One other quick thing. If you do open up an apk, be careful messing around with files named 9.png or any others that have black borders around them. You don't want to remove that border.
EDIT: Oh, one more thing. If you can find it on xda, use apktool 1.3.1 instead of the latest (1.3.2). The latest seems to have issues recompiling apks.