If bottle-conditioning is completely finished, there's no reason it won't be ready to drink as soon as it's cold, if you're only considering carbonation. The amount of CO2 in solution is indeed determined by temperature and pressure, but since we're talking about a closed system, the total amount of CO2 inside the bottle can't change once it's there, it can only move between the gaseous head-space and the liquid.
Accounting for both the different solubility and density of CO2 with changing temperature and pressure is somewhat complex. For example, some quick math shows that when aiming for 2.65 volumes of CO2 in the finished beer, there are ~0.03 grams more CO2 in the bottle's head-space at 65° than at 45°F (at equilibrium; 0.134g vs. 0.104g, respectively), assuming a head-space of 25cm3. As the temperature drops and the solubility increases this extra gas will take time to reach a new equilibrium with the beer. BUT...
...that extra amount of CO2 which eventually moves into the beer accounts for an increase of just 0.04 volumes, or 1.5% of 2.65 vol. A highly skilled trained taster probably couldn't differentiate between the same beer at 2.61 volumes and 2.65 volumes.
So, technically, yes the ideal time would be long enough for the new equilibrium to be reached (perhaps a day or two), but the reality is that the difference is pretty much negligible.