It would make an interesting calculus problem.
The things to consider are:
1. Tank pressure is dropping as you go deeper and dive longer. With the lower tank pressure you have less total pressure drop and less adibatic cooling as the air pressure drops from tank pressure to ambient pressure.
2. Ambient pressure increases at about .5 psi per foot so as you decend from the surface to 100 ft the absolute pressure inside the intermediate air passages in the first stage will increase from about 140 psi to 190psi. That is a big percentage increase, but in the grand scheme of things, it is not much of an increase compared to changes in tank pressure - at least in terms of reducing adibatic cooling. (see #5 for the major issue this causes)
3. Water temperature may drop - a little to an awful lot depending on the body of water. I have seen a 1 or 2 degree difference per hundred feet in the ocean and I have seen the temp drop from 75 to 35 in a hundred feet in an alpine lake. As the water approaches the freezing point, the lower temperature gradient makes heat transfer from the water to the regulator less eficient. in my experience this starts to become critical when the gradient falls below about 10 to15 degrees depending on the regulator
4. Gas consumption increases with depth. At 100 feet you are using breathing gas at 4 atmospheres of pressure and that increase from 1 to 4 ATM has a linear effect on the adibatic cooling load placed on the regulator.
5. The increased intermediate and ambient pressure has no impact on the number of cubic feet a free flowing first stage will produce, but it does have a significant impact on the amount of flow a freeflowing second stage has at depth. The higher intermediate pressure upstream of the orifice combined with the higher ambient pressure on the downstream side of the orifice acts like a turbocharger and allows more mass to flow through an orifice of a given size at depth than at the surface. At 100' you will probably get about a 60% increase in flow volume compared to the surface.
6. The gas itself is "thicker" and more viscous but the effects of increased viscosity in air do not begin to become noticeable until you get upwards of 300 psi / 600 feet in depth. If you are at that depth on scuba, you got big problems even without a freeflow.
Of these factors 3 and 4 are the biggies in terms of promoting a freeze flow. # 3 is a given as if the water is codl enough it can cause a freeze flow just below the surface, while #4 can result in a reg that is otherwise well behaved at the surface freeflwing at depth. 1 and 2 will actually work to reduce adibatic cooling and 5 is only a factor once the freeze flow starts - but can be significant for two reasons. If the reg falls out of your mouth at depth (cold lips) with a flow vane set so as to produice a continuous freeflow, the greater flow at depth can quickly produce a freezeflow. I have also seen freeze flowing regs stop freeflowing on ascent due in part to warmer water and improved heat transfer and in part to the reduction in freeflow volume (and the reduction in additonal cooling that results). 6 is not a factor until you are already in serious trouble due to depth anyway and if you are at 600' intentionally you are on a helium mix and helium flows through regs much easier than air anyway, so it is back to being a non issue.
