The only real avalanche concern for today would be in the highest steep north facing slopes. Old snow from earlier this season has been sitting around on these slopes and has become very weak. It's unclear if the current storm will add enough snow on top of the old weak snow to create an unstable situation. Also, the old weak snow is spotty in distribution, some slopes have enough to be a problem, some don't. The most likely spots to find trouble would be on steep north facing slopes above about 9800' in elevation from about Staker Canyon south through at least Ephraim Canyon.
In general, even with the new snow, travel is still difficult and very limited. However, if you are getting out to check out the new snow, approach those high north slopes with caution.