Me being who I am, I didn't get around to this for quite some time. When I finally did, I discovered that it was even trickier than I'd anticipated.
I had realized that, since I didn't have a tripod, I would be taking each picture at slightly different heights, and with a fair amount of overlap on each one. So I expected to have some trouble lining them up. What I hadn't realized is that I'd also be taking each picture as slightly different distances -- this picture might be a little closer to the horizon than the next one, and so on. So I'd have to shrink the closer one a bit to make the scales match.
Also ... the exposures varied. Wildly. Each shot would be noticeably and markedly brighter, darker, bluer, whatever, than the adjacent ones. At first, I didn't think that I could fix that -- then I realized that my paint program is called PHOTOpaint for a reason, and that it does have tools for adjusting hue, saturation, intensity, contrast, brightness, etc.
What it doesn't have, as far as I know, is any way to automate this process so that the computer will change picture alignment, scales, and colors for me. Kirzen said that he had software for this, but since I am me and therefore stubborn in stupid ways, I spent time eyeballing all of this on my own and putting it together.
This is the first one, and it was only a 180 or so shot; I think there were trees or something dull blocking the horizon on either side. I did a little airbrushing on the sky to try to smooth out the lines where the pictures overlapped. You can click the image to get a larger version if you want more detail.