Does my extension cord have too much internal resistance?
A few relevant facts:


The maximum current of the extension cord is the current where it produces some specified temperature increase above ambient, possibly 10 or 20 degrees C. (Or some specified voltage drop from one end to the other, hopefully not more than 10 V).
Snow is a fairly good insulator, so once it has covered the extension cord, all the heat produced by the cord will be contained around the cord. This means the cord temperature will rise more than it would if the cord were surrounded by air.
Snow (typically) falls only when the air temperature is in a fairly narrow temperature range around the freezing point of water. So it won't normally take much added heat to start melting new-fallen snow.


These three facts mean that what you saw does not necessarily indicate a problem.

But of course you should make sure the current load is no more than the cord is rated for, and that the two ends of the cord are both well protected from water intrusion if you're going to use it with snow falling or on the ground.