Even with hydrogen, the tank weight is quite small compared to the content weight. For some examples, you can look here (you may need to do some math to get the actual numbers):
You are right that the heat loss is less of a problem for larger tanks, but structural integrity, especially when facing the aerodynamic forces of launch, becomes a larger problem.
Transporting liquid hydrogen to the moon is probably not a good option. Apart from the high tank volume and weight (compared to other fluids) it also boils away very quickly under thermal radiation. On a path to the moon, the spaceship has to coast for several days, all the while losing fuel.
This usually works the following way: The tank is kept at a certain pressure. If this pressure is exceeded, a valve opens to vent some gas. This way the liquid is constantly boiling: If a bit of heat enters the tank, a bit of hydrogen evaporates and escapes through the valve. The amount of evaporated hydrogen is the entered heat over the specific evaporation heat of hydrogen at its current pressure.
Let's say we set the valve to a higher pressure. Then the hydrogen would keep boiling, and thereby pressurizing the tank, until that higher pressure is reached and the valve opens again. Now we have a bit higher temperature on the tank because the boiling temperature rises with pressure (up to a certain point). Therefore there is less of a temperature difference between the cold hydrogen inside and the solar radiation on the outside and less heat will enter the tank. However, we need to build a thicker tank, and this is generally not worth it. As seen in the document linked above, hydrogen tanks are designed to operate at a modest pressure level of a few bar. (and even this pressure is not because of the temperature in the tank, but because of the pressure requirement of the pump inlet)
The general idea to bring fuel to the moon may be viable, although a lot of energy would be needed to generate sufficient amounts of oxygen for propulsion.
That is unless there is abundant water on the moon, in which case generating fuel and oxidizer would be simpler, but that is still under discussion.