You've hit immediately on the difficulty with the 'squire' strategy. It works only on one condition, that the random encounters the 'squires' will have near the entrance to the dungeon will not be nearly as difficult as the encounters in the dungeon.
In general, I've never seen taking the henchmen into the dungeon work. Eventually everyone has to make a saving throw, and the henchmen dies. But the same tends to also be true of mounts as well. Mounts are a pain in the dungeon, and rarely survive it. So the best reason for having 'squires' is to protect the mounts, and preferably the mounts include some semi-intelligent beasts that can help protect themselves. Generally speaking, if a henchmen soaks up more buffs and healing resources to keep them alive than their contribution mitigates the need for, you have to keep them out of the dungeon because they aren't an asset but a drain on the party.
Generally speaking, if you want to keep your squires alive you have to a fair number of them, and be fairly generous with them in terms of sharing XP and treasure. This might not work in some modern adventure styles like a 3.X or Pathfinder adventure path where the PC's rate of leveling and wealth advancement is so tightly and necessarily controlled. But in an more open and less linear adventuring environment, and in particular when the amount of gold you pull out of the dungeon determines the amount of XP you get, squires can be invaluable because any shared XP is more than made up for by the efficiency with which you can pull gold out of the dungeon by depositing it with the squires and the rest of the baggage train.
The ideal set of 'squires' is a mini-adventuring party all on its own, ideally complete with its own arcane and clerical resources. The function of this mini-adventuring party is to set up and protect a base camp near the party's intended destination, and protect the mounts and baggage as well as give the main party a fortified position to fall back to in the event of retreat. The idea base camp is concealed and defensible. A small ruins or cave or other lair near the main dungeon having been previously cleared of monsters makes a good base camp. The party should immediately begin fortifying or concealing the position by camouflaging it (permanent illusions?) or building simple traps and improving the fighting position near at the entrance of the lair to give early warning of anything that might sneak up on the position. This is always a difficult decision, and there is no perfect solution, since you never know what the DM will decide has come along and whether hiding the lair entrance makes it more noticeable or less, or having traps tells something wandering casually by that something important is up when they might otherwise go along their merry way. Many of the decisions a sniper team has to make in hostile territory are applicable, though keeping in mind that its highly unlikely that the 'squires' can be as stealthy as a two man sniper team - nor can they just move around freely if they fear discovery. Judging the capabilities of the squire and the sort of enemies that they might attract can inform these decisions.
Players can reasonably expect that the base camp will suffer random encounters at roughly the same rate that the party would in the same circumstances. An encounter every few days or nights is typical. The bad news about this is that the squires might die. The good news about this is that if they don't, they'll level up faster. A reasonable DM will take into account the precautions taken by the base camp on a case by case basis. Some DMs will run the combat more or less in their head, making decisions about what likely would have happened. Others may actually allow the PC's to run their squires encounters when they happen, particularly if none of that amounts to spoilers and they have a fair amount of trust that the PC's won't metagame.
I'm quite certain by experience that the 'squires' concept works in 1e/2e AD&D and similar old school systems. I'm much less certain that it works in 3.X or later games, simply because I've never seen it work but I've also never seen it carried out well by an experienced party. I do know that it is in some ways harder to carry out in 3.X than in earlier games, because of the different ways that characters level up in the more modern games. The amount of XP required to level up in 1e/2e was exponential, so that squires quickly 'caught up' to the PC's in prowess if they survived. If you had 1/4 of the XP of a PC, you were not that far behind them. Even taking only half shares of XP and missing out on many encounters, squires could get quite potent on their own - so much so that squires were often considered replacement PC's or secondary characters that a player might eventually turn into primary characters if the primary died or entered semi-retirement after obtaining name level. But XP in 3.X and later editions if you have 1/4 of the XP of a PC, you might not be able to contribute to the party at all.
