I'll just give you the conclusion from the outset, and this is for everything from cast steel to PM-V11. Cryogenic treatment trades a little bit of tool toughness for additional hardness, and on some steels, adds forgiveness to the heat treatment process if the regular heat and quench would otherwise leave a lot of retained austenite.
Austenite, as you recall, is the non-magnetic form that occurs when you heat steel. We want to convert that to martensite and then temper the martensite. Tempered martensite is a stable and crisp structure. If steel is overheated in some types - A2 or 52100 being two - the quench may result in retained austenite. For 52100, in general, retained austenite can lead to higher toughness (harder to break) but it also has an undesirable effect in woodworking that hardness is lower. High toughness and low hardness results in a rolling edge that is very persistent.
Just as an aside, there are few steels that have no retained austenite, but a very simple steel quenched in brine or finished in cold water can achieve no observable austenite. None is an idealistic goal, but the resulting tool in use is more important than hitting theoretical goals.
So, What is Cryo Treatment?
Typically, it is a liquid nitrogen bath and occasionally another concoction at a very low temperature. It is most useful if used after steel is quenched and before tempering, though more complex steels may introduce liquid nitrogen treatment between tempers. Those are outside of the scope for hand tools.
Toughness is a term often used along the lines of "that cryo treatment makes steel really tough". It's not reasonable to expect woodworkers or even retailers to know the difference, but toughness is typically a measure of energy required to break something. Strength or purposes of woodworking tools is a measure of how much force it takes to deform or damage in general. If an edge rolls or a knife bends, they have not met their toughness limit, but they have failed having enough strength. Knives and lawn mower blades and other items of the sort rely on toughness to avoid breaking, but for woodworking, we prefer a lot of strength with enough toughness. No edge rolling, or anything like that - the stable edge remains in the same shape and just wears.
Cryogenic treatment improves strength (due to increased hardness), which leads to a question. Is it ever not better to do it? If you're chasing hardness to the nth degree and the process without cryo would result in an edge that doesn't chip or roll, but with it, the edge chips, then it doesn't really serve any purpose. Too, steels like W1 and 1095 can be fast quenched in a garage shop such that very little or no observable retained austenite remains. It's unlikely cryogenic treatment will do anything in that case, at least anything noticeable in steel hardness. Commercially, if you apply this to O1, that would also seem to be the case, but a harsh cold-end and fast quench is something probably not done industrially, so a cryogenic treatment on a somewhat incomplete quench could still lead to a more crisp feeling iron.
My view if buying tools - what do you want to get if all other things are equal:
1) A2 steel - cryo treatment every time
2) O1 - on the hock france iron, there's nothing really to improve with it. On other O1 irons that are less hard, the cryo treatment may be useful, but O1 seems to be getting phased out of commercial use
3) turning tools? Cryo treatment every time
Other side Comments - Especially in Regard to Quality
you can peruse heat treatment discussions at knifesteelnerds.com, the site operated by Larrin Thomas (a legitimate metallurgist and formulator of several good alloys). If you review the heat treatment schedules and test results of different soak temperatures, you'll notice that without cryo treatment, the temperature range for good results can be quite narrow. Overheating in the soak before quenching can fall off of the table due to excessive retained austenite in a short range. Put differently, if a heat treating service misses for any reason, overheating by 75F on a soak could result in a mediocre tool. Cryo treatment after quench, even after long idle time since heat will convert some large fraction of the retained austenite to martensite. The result? Instead of perhaps a 50-100F range for ideal results, the range can increase significantly, especially on the side of accidental overheating and instead of the overheated samples being softer, they end up often being harder.
That is, the Cryo can repair sloppy efforts elsewhere in the process. Peters or one of the other large heat treatment groups advertised recently that Cryo is now standard in a lot of cases where it used to be an add-on option. I think this is for their benefit as much as it is the customers. Less contesting results by customers, and liquid nitrogen isn't expensive - it's a byproduct. It's expensive to you and I if we are getting a dewar filled with 20 pounds of it at retail - at least expensive if you aren't using it pretty quickly and it dissipates into the atmosphere. LN isn't like a jar of water - site storage in a dewar requires venting and it may last 3 days or 3 weeks, but you lose it even if you don't use it.
What about other claims - like enormously increased wear intervals. The biggest boast I've ever seen on a plane iron is an M2 plane iron that touted up to 22 times the edge life of "typical plane irons" or something of that sort. M2 lasts somewhat longer than A2. If there's a differential in hardness where the M2 is very hard and the A2 is lacking, it could be as much as twice. 22 is a bizarre claim, but most of the information about metal properties in woodworking ad copy is bogus, and a lot of the terminology is wrong. Cryo won't do too much for wear unless it's correcting a flaw like the one mentioned above where steel is overheated prior to quench.
In the context of most of what you will do making your own tools, unless you are cutting A2 irons and sending them out for heat treatment, you can use a relatively plain steel and focus on limiting retained austenite and match hardness results on heat treat sheets with cryo treatment without actually having to use it.
Are any vintage tools lacking because of the absence of liquid nitrogen? No. They aren't a type of steel that would've benefited from it, so don't fall for any kind of explanations of "new tools are better than old tools because of things like superior steel with fine grain and cryogenic treatment". The grain in cast steel tools from 1875 is far finer than anything made from A2, etc, but A2 is far easier to heat treat without skilled staff.