I see this said a lot, but the math doesn't bear this out.
A first level character with Plate and Shield, fighting low level monsters (need a 17 to hit - or 20% chance), who do 3.5 points of damage per hit, basically do .7 points of damage a round averaged over a long term.
A character with 5 hit points thus survives on average just over 7 combat rounds, while a maxed-out character with 8 hit points lasts just under 11 1/2 combat rounds.
In my experience, this difference has been too little to notice over the long
term. Survival at low levels, in my experience, is much more tied to whether the character can afford to purchase plate mail at the start...
A first level character with Chain and Shield, fighting the same monsters (who now hit 30% of the time and thus do 1.05 points of damage a round) only last 7.6 rounds at max hit points, or a little less than half a round longer than the 5 hp character with Plate and Shield. (The 5 hp character lasts about 4 1/2 rounds.)
It's curious that I often see people give out max hit points at first level while simultaneously making plate armor more expensive.
That's one of my few problems with the Labyrinth Lord clone of B/X. While giving clerics 1st level spells (which, assuming that spell is CLW, essentially gives one character an average of 4.5 additional hit points per session), it makes plate armor too expensive for first level characters. In the long term, that's going to make 1st level play much more deadly, even with the added cleric spell.