Yep.We always houseruled max HP at 1st level and even then death was common from wounds at low levels. The only real upside was that character creation only took a few minutes.
There's a real assumption in early D&D that you're playing quite often, so that low-level characters get plenty of opportunities to play. Eventually you get one that survives, and that one becomes famous and beloved.
I think combat is as frequent in oD&D and AD&D as in later editions; it's just that you pay a lot more attention to how difficult things are. Running away if it goes badly is more accepted as a tactic, and there are some encounters you avoid altogether. However, that doesn't take long and you're into the next combat quickly.

Once most of the party is a few levels higher (definitely by 5th), new 1st level characters gain XP a lot quicker, and so don't have to put up with low hp for as long. Sure, they're up against tougher monsters, but not that much tougher.
Cheers!