This doesn't really strengthen your back, but it may help you. My back
is lousy, too, and the best thing I've done is this:
While trotting or cantering, put your reins in one hand and then stretch
the other hand skyward and totally stretch out your back. Switch hands
and do the other side. If youhave someone to longe you, you can do it
with both hands at the same time. (I have one horse where I can knot the
reins and do it without a longe line). Makes my back feel graet and it
also does wonders for your equitation!