The small amounts of recent new snow and anticipated snowfall during the day coupled with an overall cooling trend point to a mostly LOW overall avalanche danger today. Keep in mind that there is always some danger of avalanches in the backcountry especially if you choose to get into steep radical terrain or are lingering in confined terrain such as gully bottoms or couliors.
A natural wet snow avalanche, especially a glide avalanche that breaks to the ground is the biggest threat of a large dangerous avalanche. It is not wise to travel for more than a short period of time in the bottom of any drainages or gullies that have larger steep avalanche paths above them. If you avoid doing this, you'll most likely avoid any serious wet snow avalanche concern today.
Any new snowfall that occurs during the spring can be unstable especially when it's falling. It generally stabilizes fairly rapidly but it can become unstable again as it heats up for the first time. Pay attention to how sensitive the new snow is during periods of snowfall and then make sure you're not in confined terrain or below obvious avalanche paths if things heat up and become unstable after the new snow falls.