NOAA predicts today's highs at the Portal and the summit to be 64 and 46. I'd say the snow will be melting fast! No need for snow shoes, unless you want to sweat more due to the weight on your pack.
As for water, I am sure you will find running water. This
was written yesterday regarding Chicagosky's trip report of April 6-8:
We met very briefly at UBSL. You were holding a water filter; I pointed you to a source of unfrozen water near the UBSL outlet. We were the three guys building a snow shelter---also a part of the Caltech group.