Disclaimer: I am not a meteorologist.
Snow forms when supercooled water droplets nucleate onto particles in the atmosphere. After forming, they grow further by both tumbling around within the cloud and by tumbling down through the atmosphere, colliding and mingling with other snowflakes throughout their way. At journey's end, the snowflakes aggregate on the ground or whatever surface they happen across, building snow cover.
From my own understanding, there are a few factors in this process that are dependent on gravity and air pressure.
I suppose the first thing to consider is that an atmosphere of greater pressure may have a greater water vapor partial pressure. (This, incidentally, leads to water having a higher evaporation temperature, which is a whole can of worms we don't have to open. For more information, see this question). The takeaway from this is that the boiling point of water increases while the freezing point stays close to its original figure of zero Celsius, and that the atmosphere may retain more water for its greater pressure than otherwise. (Equations for estimating vapor pressures, if it's relevant.)
A second thing to consider may be the effect of both lower gravity and greater air pressure on a snowflake after it has formed. With lower gravity, the snowflake takes more time to fall through the atmosphere, probably increasing the rate of snowflake-snowflake collisions. Simultaneously, the greater air pressure is responsible for greater drag on the snowflake as it falls, slowing its descent further (I am unsure how this affects the rate of snowflake collisions). With this, I think it is important to note that, under lower gravity, clouds may tend to form higher up in the atmosphere and may tend to be taller, giving snowflakes even longer travel distances. See this question.
A third thing that may need consideration is the effect of a lower gravity on snow cover aggregation. Under lesser gravity, snow might be lesser inclined to compact itself on the surface.
What could snow be like on a low-gravity and high-pressure world?
A general case answer is acceptable, one which describes the snow and its various meteorological changes associated with raising atmospheric pressure and dropping gravity.