In my experience, cold soil may very well result in non germination, but if they do germinate and come up, they will so no signs whatsoever of having had a cold start. In other words, if they DO come up, they will do just as well as any other seed planted in that location at a warmer time-assuming the weather does warm up and of course it will eventually. But like Ray said, might as well replant. Why wait a week or more for seeds that may be doomed at this point, when you could plant new ones and they can be developing and growing during that time for sure.
BTW....while it is 100% definitely true that planting watermelons in cool soil can often lead to them rotting before they germinate, what blows my mind is that every spring I get a lot of volunteer watermelon plants out in my patch. That means that those seeds laid there in my garden while the melon they were in completely rotted away, then they laid there in the cold, wet winter soil for about 6 months...then all of a sudden they sprout up in the spring. Its crazy. Life finds a way. BUT there are thousands of seeds in my patch at the end of the year and only a few dozen sprout, so it wouldnt pay to play the odds or count on seeds in cold soil to sprout.