I was always yelled at by my father when I was first starting to drive when I left the A/C on when I turned off the car, and then later turned it back on, with the reasoning that I was ruining / decreasing the life of my engine. Is this true? (I currently drive an '03 Chevy S10, if that matters, though I'm more interested in a general answer).
Not at all. You may be in some small way reducing the life of your starter, but this would be pretty negligible.
When you start with the A/C switch on, you will be starting with the A/C Compressor clutch engaged, which means the starter must turn both the engine and the compressor; altogether a rather trivial amount of force in comparison to the force needed to spin the motor with the compressor clutched disengaged.
Once you've gotten it started, the compressor would be robbing some non-zero percentage of the motor's power, just as the alternator and power steering pump would. One could argue perhaps for some reduction in fuel economy during the startup process, but hey you've got a cold car to get into.
To put this in perspective, think of hotter climates like Arizona. Most cars have remote starters, and the leave their A/C on full time so that when they start their cars from inside their house, the cabin is a reasonable temperatures. I'm also convinced that engines in those climates last much longer than those from colder ones, due to less extreme temperature transitions.
On anything post 1997 i've seen, when the starter motor is engaged the A/C clutch is disengaged and any non-essential electrical loads are automatically turned off until the engine is actually running. It makes no difference. On an older car the only difficulty is going to be starting a cold engine and if it was cold, you wouldn't have the A/C on in the first place :)
Your dad may have gotten confused with the issue of starting with the heat on can make the engine take longer to warm up to running temperature.