Snow appears to burn because of the chemical properties of water and the physical makeup of snow. Snow is loosely packed and contains more air than water, which creates a cushion that slows down the rate at which the icy structure melts.
When a flame is held against snow, the outermost layer melts and wicks the moisture away from the contact point. Because snow is comprised of mostly dry air, it becomes water saturated as it melts and turns into slush. The conversion of dry snow into wet snow is slow enough that snow appears to burn when a flame is applied.
The other effects of snow burning, such as the smell produced and blackening of the surface, can be explained by the incomplete combustion reaction that produces the flame in a lighter or blowtorch. Incomplete combustion occurs during situations in which there is not enough air to facilitate a combustion reaction. This problem can occur in a lighter or blowtorch because of the small chambers in which the fuels are ignited. Soot is the deposited remains of the carbon that didn't completely react. Some unburnt fuel is released as an odorous gas, and toxic carbon monoxide is often present.