Under battery meter it looks like display is the big battery hog. Will a solid black wallpaper make any noticeable improvement compared to a bright colorful one?
Only if your phone has an AMOLED display. If it has an LCD display, the backlight is on regardless of what color is being displayed. But with an AMOLED display, each pixel is a light source that is adjusted independently, so displaying a mostly black screen does reduce power consumption.
That said, how much time does your phone spend displaying the home screen (which is the only time the wallpaper is displayed)? Probably very little. Most of the time you’re using full-screen apps. So I doubt it would make much difference in real life.
I don’t know if any phones do this but some LCD TVs and monitors will dim the backlight during dark scenes as a way to improve contrast and black levels, which also reduces power consumption. But, as you said, if you don’t have the wallpaper displayed by itself much it doesn’t do much (sort of like asking if a screensaver saves power; even with old CRT monitors even a blank screen (but still on) doesn’t reduce power much, maybe by 10%, since most of the power isn’t used by the CRT itself; a complex graphically intensive screensaver may even increase power used by the CPU and GPU).
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You can extend your battery life greatly by turning off or not using everything that makes your smartphone worth having in the first place. 
It won’t help you (and you don’t say which model you have), but checking reliable battery-life tests is an important factor in choosing a smartphone. Some, like my Evo 4G, practically needed to have a plug-in power cord. Others, like most newer ones (including the S2, S3, probably the S4 and the Note/Note II) have extremely long battery life. It’s not much fun having a mega-power phone you have to shut everything off on to get a day’s use out of.
Search for a good power-saving article on your specific model. Someone has likely already done the homework for you and can tell you what settings to use for maximum battery life with minimum downside.
I’ve seen hacks (requires rooting the phone) where you turn off the red and green color channels for all apps. It makes things a little hard to see, but it’s a big reduction in power consumption :).
At my last company, I had a few vendors present this technology - dynamically adjusting the backlight based on the image on the screen. It’s pretty cool, and does give a noticeable savings. I’m not sure if anyone is shipping a product with it.
Another way to save power in the display area is to reduce your backlight. Most phones will allow you to tweak the backlight level.
Why the red and green, specifically? The resolution of the human eye is worst in the blue channel, which would make that a particularly hard-to-read choice. Turning off the red and blue (leaving green) would be much easier.
Just a guess, but most amoled screens are pentile instead of standard RGB, and iirc there are twice as many green subpixels as red or blue. Shutting off red and green should get you 75% screen power savings, where shutting off red and blue would only get you 50%.
I meant to say green and blue, in fact. IIRC, the reasoning was that red OLEDs are more efficient than green or blue, but I don’t know that it was thought through all that well.
Gorsnak is right, though–there’s generally twice the number of green subpixels, so there’s less theoretical savings if you keep that.
One small addition–in my LED color mixing experiments, I’ve found that even though the *resolution *is poor, the eye is actually quite *sensitive *to blue. Something like 15 lumens of blue is perceptually equal in brightness to 80 lumens of green. So there’s some value in using blue, though OLEDs have the problem of poor efficiency and lifetime for that color.
I have an AMOLED display and I like it turned up all the way. It takes up 50% of my battery. I make up for it by keeping GPS off unless I need it, Bluetooth off unless I need it, and I don’t let it search for WiFi unless I need it (which is pretty much never). So still get a long day out of my battery (SG2). I’m sure it would be much better if I turned the display brightness down by even 25%, or set it to go dark after a minute, but I don’t. I just plug it in to charge on the nightstand every night since it’s my alarm clock, too.
Since OLEDs degrade as they’re used, won’t this screw up your display when you DO want full colour? Now all your reds won’t be bright enough.
I have a smartphone with AMOLED display and a lot of apps and I mean a lot use black background. I also use Windows Phone operating system so maybe phones that come with WP also usually use AMOLED, so that’s why WP apps are often optimized for it.
Well… sorta. Blue already degrades much faster than the other two colors, so there will be a color shift no matter what you do. In principle, you could change which color you show in order to maintain the correct color balance over time. Load up a “white” screen, say “oh, that looks greenish”, and then show only green for the next N hours :).