I think that "old school" is a completely subjective label. Everyone has different experiences in playing D&D, and it's foolish to claim that there is anything resembling a monolithic expression of the game.
This is true or not true, depending on whether you're talking about your definition of old school (which is based on how the world interacts with the players) or whether you're looking at the way the rules operate. More on this to follow.
I think that, for me, "old school" means:
1. Player choice drives the game.
1a. Really bad player choices lead to TPKs.
1b. Really clever player choices lead to rewards and advantages beyond the norm.
2. There are strains of an almost Lovecraftian incomprehensibility to many gods and demons, a la the chaos temple in Keep on the Borderlands.
3. The forces of evil gather on all sides of the Realms of Man.
That's pretty much it, to me. Rule 1 and its sub-rules are the critical parts of it. Quick, creative thinking is key. Mindlessly attacking is a fool's gambit.
I'd agree with this, and also agree that this part of "old school" is actually quite subjective. These items "emerged" from the rules as they existed in the early days, from the literature that happened to be on shelves in the early days, and from gaming advice in The Dragon Magazine. In other words, a historical phenomenon that might be more or less true depending on the group. This was a zeitgeist, but not a universal mode of play.
ON THE OTHER HAND, and this points out where the term "old school" is not a great term because it's too broad, there's also an objective fact, which is the condition of the rules. Sparse and vague. This actually implies a mode of play, commonly called DM fiat - a pretty decent descriptive term which is unfortunately loaded with negative connotations. But it's nevertheless accurate as long as one remembers that the players and DM are playing a game and the players won't let a terrible DM get away with consistent unreasonability.
Vague rules effectively give the players only a few "rights." The DM makes rulings on the fly, and isn't "tied" to using a consistent method time after time. It's for this reason that "old school" is a distinct gaming style supported by old (or old-style) systems ... just as later games are a distinct gaming style in which the DM operates in a framework that lets him game a bit more head-to-head with the players. Both are fine depending on what the group likes - but OD&D is absolutely not just 3e or 4e "lite." It's a different animal entirely. Here you can make a fairly definitive statement about what old school means, because everyone was using those vague rules and was forced to use the free-form old school gaming style. The fact that everyone was forced to play that way doesn't mean it sucked - it just means there was another approach waiting to be born. In fact, I think there was a third style waiting to be born as well - the "explore your character's mind and simulate it" school that dominated 2e to a certain degree. All three styles work for different groups, but they are definitely distinct "games" operating on different principles and to a certain degree each style is complemented by its particular set of rules (3e/4e and 0e tend to support their play-styles rather better than 2e, I believe).
If anyone's interested in seeing 0e distributed as a toolkit for adding new features from the ground up, take a look at
Swords & Wizardry, which is a 0e retro-clone I wrote, but which is part of a larger project to take gamers back to the hobbyist attitude of tweaking and screwing around with every facet of the game. Example: in the S&W rules themselves, there's a dual stat built in for ascending/descending AC. It can be used, and is compatible, both ways.
EDIT: S&W is distributed in .doc format as well as pdf specifically to allow cutting and pasting for house rules, and it's all OGL.