There are several aspects to sowing with either first frosts, last frosts, and on snow.
Sowing in the late fall frost gives the seeds a prolonged chill, and then the winter snows give them insulation, so they are warmer and might germinate under snow.
Sowing on top of snow is also done which gives seeds a chill, and also moisture so they are ready to germinate when weather warms. Sowing on top of snow also helps the gardener to distribute the seeds better. It also prevents critters from getting most of the seeds.
Sowing with the last frosts gives seeds a light chill which may encourage the breaking of dormancy too.
Try to find information on where seeds originated naturally so you duplicate the amount of chill they require. The data bases are good too. Some seeds are to be chilled between minus 4 º C and plus 4 ºC ( 18 ºF to about 40 º F ) These temperatures are when frost is likely.
