As far as I remember, yes, everything becomes brittle at low enough temperatures. This is due to the brittle-to-ductile transition (BDT - or sometimes referred to in reverse as DBT, ductile-to...). This transition is temperature dependent (amongst others (strain-rate ...)). Can every composition actually reach low enough temperatures, or do some have a transition temperature below 0K. This is also pressure- and state-dependent. Also, the BTD applies to solids.
One thing to keep in mind though, is that dense things become very hard to break, like a leg of lamb or a banana. A sufficiently frozen banana (liquid nitrogen) will break, but it requires a lot of force. Simply dropping it from a meter or two will not shatter it. It needs to be thrown or hit with something harder. Yes, I have tried this. The bigger it is, the more force it would require. I can shatter any boulder for you, but you may not have the size of hammer I would need ...
Having said that, most biological matter/tissue is mostly water, so freezing the mentioned examples would result in some form of ice. At least something that should behave similarly to ice. The DTB-transition applies generally, like for your desk or computer.
As far as I know, the BTD-transition is not completely understood. I don't think I have my lecture notes anymore, and it is a while since I took a class on this, so I would start with Wikipedia, but you would soon end up in scientific papers, I think.
In essence, brittle fracture is due to direct bond breaking resulting in cleavage. Ductile fracture is due to microvoid growth and coalescence. Temperature sort of maps to time and information transfer. At high temperatures, particles/dislocations travel quicker and with more ease than at lower temperatures. Thus information (stress, strain, ...) travels through the sample. There is more time to move around and shift to try to alleviate the applied stress or strain. So, there is time to form microvoids and lots of stretching. These voids will grow and eventually join with neighbouring voids and so the fracture will advance.
At low temperatures, many or all of the ductile mechanisms do not have time to come into play, and at the extreme, fracture is locally advanced through the breaking of the weakest bonds.
In the DTB-transition zone, both mechanisms are present. As these mechanisms are very basic and general, I think that any material should undergo such a transition (assuming transition temperature above 0K). Of course with a varying fracture toughness and ... "shatterability".
Note: These are educated guesses at best, I have not done any calculations or simulations on this.
@MaxWilliams Firstly, this person would already be dead as all body functions would have ceased, but that's not really relevant to the question.
Now, a person is quite large, so you would need a lot of energy, preferrably concentrated. Explosives would do it (and other things), but you asked for handguns. I can not realistically imagine any handgun to do this. One point is that I think that the energy from the bullet would be dissipated in the dense body.
Another point is that the shape of a person is quite stretched (not spherical) so what you are asking for is bonds that will separate with relative ease as well as distributing energy transversally. I am assuming a shot to the torso. Maybe an extremely powerful handgun could penetrate all the way through, maybe a hollowpoint or some specially designed bullet would create more explosive damage, but in the end, I think that the target is quite comparable to a stone (maybe ice) statue, and I do not think that would be shattered that easily. Definitely not like in the movies.
