At the end of the day, the only question that matters in life is ... If a snowman farts will his butt melt ?
Snowmen do not have an intestinal tract and if they did they would lack the muscles and if they did have muscles they would lack the energy and food but if they had that then the snow would melt due to body heat and therefore there would be no snow to melt.
A snowman is an inanimate object and does not possess the parts available to create a fart. So, it would be impossible to answer this question because its physically impossible. Even if snowmen were able to fart there would be too many factors, like, the temperature of the fart, power of the fart, the temperature outside, how thick the snow is, etc.