We would expect well drained soils to dry more quickly because they will normally have less water in the soil profile. This is not always the case, in the spring many well drained soils will have a saturated profile but just not for as long a period as the less well drained soils. Sandy soils will commonly dry more quickly because they can not hold as much water as the finer textured soils. Sandy soils can be poorly drained if no outlet is available for the water. There is to my knowledge no means to estimate how long this process of drying will take on a given landscape.
Frequent observation is the only real method and that is to a degree subjective.
Decisions that a soil is dry enough are made based on a number of criteria. It is probably not practical to wait for ideal conditions. This would most likely take too long. Farmers may have to look at this as a matter of relative risk. If the planter is operating correctly and doing a decent job of planting they may have to accept some risk of compaction and the damage that it may or may not do to yields.