Way too soon to say this will be a cold spring. 4/2.
And as Jesse pointed out, March wasn't really cold, more just wet.
I think a wet summer is favored. Whether it's cool/wet, or just plain wet, will depend on the longitude of the NPAC trough, which depends on the longitude of the Pacific convection and polar mode. Unless the IPWP rapidly collapses and focuses convection on the dateline, a persistently ridgy western summer will be difficult to obtain, IMO.
The polar mode/NAM state (which is crucial in determining the antecedent NE-Pacific streamflow) hinges on the IO/ATL convection and particularly the strength of the IO/Asian monsoon, as well as the +QBO influence on the z-cells and subtropics, which sort of ties into the IO as well.
If we fall into a -NAM summer regime, that increases the chances of a cooler western summer. If we fall into a +NAM summer regime, that increases the chances of a warmer western summer, but will cool the Arctic (and the entire NH above 30N), relative to the tropics, ahead of next winter, which is a recipe for an exciting long-period wave train.
FWIW, we haven't seen a +NAM/+NAO summer since 2013.