Temperature is the key for both corn and soybean. Temperature below 28oF for a couple of hours will be lethal to growing tissue that has emerged. Temperatures between 28oF and 32oF will result in definite frost injury to above ground tissue. And temperatures between 32oF and 50oF will result in poor vigor and growth. Regardless of temperatures, the last couple of days have put planted corn and soybean at greater risk for pathogen infection. Make sure to get out into your fields over the next couple of days to assess stands. For frost injured crops, wait 48 to 96 hours following the last frost (or cold temperature) occurrence to be able to fully assess living versus damaged or injured tissues.
Yellow corn will respond to the sun yesterday and today. Water soaked corn likely won't grow, but if the growing point is still viable (cold temperature did not penetrate to growing point) the plants will have to slough of the dead tissue. A dead growing point is unlikely unless temperatures got below 28°F for several hours.
Soybean at VE to VC (up to unifoliate leaf stage) are fairly resilient to cold temperatures. Expect some frost damage to cotyledons and hypocotyl but survival is likely unless there were several hours of temperatures below 28oF. The apical meristem and/or auxiliary buds are not expected to be killed at temperatures down to 28°F for only a couple hours. Trifoliate leaves are susceptible to temperatures below 32oF.
Regardless of emergence or not, patience will be the key. Assess stands after 3 to 5 days. If above ground vegetation is dead, look below ground to check for viable growing tissue.