No, in fact I don't; my question is an honest one, and given that I have good reasons to suspect that the effects are quite complex as your research has probably also suggested, I was surprised at the apparently definitive answer
@RalphLambrecht provided. This suggested a deeper understanding of the physics and/or chemistry involved, and I would have loved to hear a little about it.
My reasoning on the subject would be that for chemical reactions, bonds need to be broken and re-made I assume are significantly stronger than the bonds you'd encounter in a physical wash process. After all, in the former case, molecules break apart, in the latter, they very crudely put only rub and stick together. I'm not a chemist, and while I'm vaguely aware of different types of intramolecular bonds and the notion that the energy required or released in breaking and/or re-making such bonds depend greatly on the substances involved, I couldn't begin to understand on that shallow basis how temperature would affect all chemical reactions as such, as opposed to all physical processes. Yes, in general, it can be expected that both will proceed at a higher pace. But can it be so easily/readily stated that the temperature dependency would be any more or less for either of these groups of processes? And/or are the differences between specific processes (chemical or physical in nature) larger than the on-average differences between the chemical vs. physical process groups? I really wouldn't know, and given the complexity involved, I'm again surprised at how definitively some appear to be able to state the relative magnitude of such temperature dependencies, and the notion that such a dependency would be much less relevant for a wash process.
I can, sort of, address this, but it will be long. Please keep in mind: (1) this is empirically-based theory; the only way one gets the rate coefficients discussed below is by measuring them, so one can't tell the OP that it's safe or unsafe to wash in cold water from first principles. You still have to do the residual hypo test to be sure. The reason I felt OK previously claiming that the temp dependence of development is stronger than that of washing is empirical: I know developing in even ~55F cool tap water is a lost cause, but that washing in water around that temp seems to be doable if you wash long enough, and Kodak makes a much bigger deal about development temperature than wash temp. (2) I'm a physicist, not a physical chemist.
Now, what is the temperature dependence of a chemical reaction? These are usually described by the Arrhenius equation,
https://en.wikipedia.org/wiki/Arrhenius_equation
k = A * exp (- E_a / RT), or: ln k = -E_a / RT + ln A
k is the reaction rate constant, A is a prefactor specific to this given reaction, E_a is the "activation energy" also specific to a given reaction:
https://en.wikipedia.org/wiki/Activation_energy , R is the gas constant 8.3 J/K/mole, and T is the absolute temp, degrees Kelvin. (You could use the Boltzmann constant k_B instead of R if you like its units better). RT has units of energy (per mole).
This is where the common saying that chemical reaction rates go exponentially with (absolute) temperature comes from. A physical interpretation is that the activation energy E_a is a potential barrier that the reactants have to overcome to complete the reaction, and at high temps, the increased energy of the reactants lets them overcome it more easily. (This is an oversimplification, but it explains a lot.) That's why even an exothermic reaction that releases energy doesn't happen instantly.
It is sometimes said, like on the Wiki page for the Arrhenius equation, that for typical reactions at room temp, an increase of about 10 deg C will speed the rate up by 2-3 times. (If you look at a developing time-temp chart, this is about right for the development reaction, +10 deg C may halve the developing time.) Let's differentiate the equation for ln k:
d ln k / dT = E_a / R * T^-2
d ln k = (dT / T) * E_a / RT
This shows that the ratio E_a/RT governs how fast the reaction rate increases with temperature, separate from the prefactor A. If I raise the temp by 10 C, from about room temp 293 K to 303 K, dT/T = 10/293, or one part in 30. If my reaction rate k increases by 2-3x, ln k increases by 1. That says that E_a / RT ~= 30. So the activation energy Ea is around 30x larger than the energy RT at ambient temp. The reaction is suppressed by a factor of exp(-30), which is a tiny number. That's why it takes several minutes to develop silver, even though we are talking about molecular processes and molecules are really small and do things in microseconds. AFAIK, the reason useful reactions happen at all is that there are a lot of molecules, so many encounters every microsecond, of which a few get over the activation energy barrier; and that the prefactor A is numerically large. (This is where a real physical chemist would explain it better.)
It wasn't actually that easy to find activation energies for ordinary chemical reactions in solution, but for example I googled this paper by N. Shinozuka and S.Kikuchi:
https://www.jstage.jst.go.jp/article/photogrst1951/1964/14/1964_14_13/_pdf/-char/ja
where they measured the activation energy of the D-76 film development reaction at E_a ~ 16 Kcal/mole. Converting the units, for 20 C (293 K) that gives E_a / RT ~ 27. So a quite typical reaction, where it has this huge activation energy E_a and thus a steep rate/temperature dependence. Generally, developers are all trying to do the same thing, reduce silver halides to metallic silver, which is why you can use the same time-temp dependence for different developers. However, some other chemical reaction could have a somewhat different E_a and different rate/temp dependence.
Okay, so that describes chemical reactions, what about physical processes like the diffusion of molecules into liquid or the adsorption of fixer molecules attaching onto paper fiber surfaces? A physicist finds the formula exp (-E/ (k_B*T)) very familiar, as most processes near a thermodynamic equilbrium have states described by something like a Boltzmann distribution with this exponential tail to high energy, and the molecules in the higher energy states are more likely to do something (like overcome the potential barrier to stick themselves to a fiber). So something like the Arrhenius equation also describes many other physical processes; the wikipedia article mentions its use for diffusion, for example.
But there's nothing that says that the activation energy for a diffusion process has to be similar to that of an ionic chemical reaction; that ratio E_a / RT is critical because it tells how steeply the rate depends on temperature. I don't know the activation energy for diffusion and certainly not for adsorption onto a fiber or film substrate; I'm sure there are several different values, because for example we all know that fixer doesn't stick to film or RC paper the way it does to fiber. I agree with what koraks said above, that it seems like intermolecular attraction (such as fixer sticking to things) would require less energy than ionic reaction, which would make E_a/RT smaller and the reaction less dependent on temperature. But that's just handwaving by me. What is important is that there is a solid physical basis for the different processes having different temperature dependencies. To say more, one would have to find more measurements of activation energies.
