Water in itself is not very conductive. Even salt water, which is far more conductive than plain water, isn't a great conductor, and I suspect would have trouble carrying enough current to melt a heavy-gauge wire such as a generator starting wire in any remotely likely scenario underneath a vehicle.
You almost certainly have an exposed part of the wire--either at an end or, I think more likely, a spot that has chafed or been pinched through the insulation--sometimes brushing against something grounded such as the frame of the RV. The snow or lack of it is coincidence, not the cause. So long as the wire is connected to the battery and the underlying issue is not fixed, you have a potentially very dangerous situation, a fire hazard.
(And yes, a wire will heat more where there is a poor or poorer connection, but it won't heat at all if no current is flowing through it, such as should be the case when the generator is just sitting there. Even a very good connection--or the wire itself--will get plenty hot if there is sufficient current. If the connection is not protected by a fuse near the battery, you would be very well advised to add a suitably sized fuse as well.)