When you do some sums, you find that the total energy involved in vaporising and re-condensing the total amount of water to form a cloud is pretty enormous. Although one could produce some local heating and re-evaporate a small region of the cloud, it would involve a vast amount of energy to make a significant effect.
Using a laser /maser for this sort of exercise is not, actually a good approach because they are very inefficient devices. Better to use the energy directly in the form of an electrical element or a microwave transmitter, focussed with a dish reflector. You don't need a laser thickness beam, in any case because it would soon be scattered.
The problem is not unlike what you encounter in your bathroom on a cold morning, after taking a shower. You need the bathroom heater (say 500W) on for about 15minutes, to make any real difference to the 'steaminess'. That suggests the need for many kW, if you wanted to tunnel through a cloud effectively. If this were feasible, Fog Dispersal Systems would surely use the method everywhere. The only method that seems to work seems to be to burn tons of fuel around the runway and I think that is only done on rare occasions, if at all, in practice.