public static List<SnapMode> SnapModes {get; set;}

//Get the current snapping modes
foreach (var snappingMode in Snapping.SnapModes)
  { ... } // do something for currently set snapping modes
  
//Set the current snapping modes
var modes = Snapping.SnapModes;
Snapping.SnapModes = modes;

// set only Point and Edge snapping modes, clear everything else
//At 2.x - ArcGIS.Desktop.Mapping.Snapping.SetSnapModes(SnapMode.Point, SnapMode.Edge);
ArcGIS.Desktop.Mapping.Snapping.SetSnapModes(
  new List<SnapMode>() { SnapMode.Point, SnapMode.Edge });

// clear all snap modes
//At 2.x - ArcGIS.Desktop.Mapping.Snapping.SetSnapModes();
ArcGIS.Desktop.Mapping.Snapping.SetSnapModes(null);


// set snap modes one at a time
ArcGIS.Desktop.Mapping.Snapping.SetSnapMode(SnapMode.Edge, true);
ArcGIS.Desktop.Mapping.Snapping.SetSnapMode(SnapMode.End, true);
ArcGIS.Desktop.Mapping.Snapping.SetSnapMode(SnapMode.Intersection, true);

// get current snap modes
var snapModes = ArcGIS.Desktop.Mapping.Snapping.SnapModes;

// get state of a specific snap mode
bool isOn = ArcGIS.Desktop.Mapping.Snapping.GetSnapMode(SnapMode.Vertex);