Wet snow avalanches are your main concern at this time of the season. These generally don't pose much threat to people. The rule of thumb for staying safe from wet avalanches is if you find yourself in areas where the snow is super wet, slushy, sloppy and unsupportable to the point where your boots are sinking deep into the wet snow, stay off of and out from underneath steep slopes. Also, stay out of gullies and ravines with steep walls. It's fine to go out and enjoy the wet snow but don't overstay your welcome later in the afternoon when things are really wet.
The typical springtime cycle is the snowpack becomes stable overnight when the surface freezes and then it becomes more unstable during the heat of the day as it gets wet and sloppy.