This question asked several times and answered clearly by Dr.Clark and others. I will show you some answers:
1. Snowman formation is caused by some of the flux in the clinker remaining as a liquid after the clinker falls into the cooler. The root cause solution is therefore to achieve more cooling in the kiln itself. There are numerous solutions to the problem of the removing the snowman itself. Blasters are the most commonly used method. Alternatives are acoustic cleaners or Denko´s "pusher".
2. I am unaware of the use of silicon carbide blocks to ease the removal of snowmen, and therefore cannot give any references. I also do not think there a value for LSF, SM or AM which will avoid the formation of snowmen. Snowman formation is caused by a complex interaction of the clinker chemistry and process conditions in the kiln & cooler. The chemistry cannot be considered in isolation. However you might expect that a higher silica modulus and alumina modulus will lead to less snowman formation as the amount of flux in the kiln will be reduced. Other factors to consider are the alkali and MgO content of the clinker and also the secondary air temperature and its stability.
3.A snowman is the formation of a large build-up on the first grate of the cooler where the clinker falls from the kiln rather than a build-up in the kiln.
I hope this answers answered your question
Best regard