Covering plants for the winter: bleg

So, I’ve been, slowly, covering the various containers and beds with straw for the winter.  The weather was warm enough that various things were trying to sprout.  Picked up what should be my last needed bale of straw yesterday to finish up.  Of course it was raining by the time I got home, so I didn’t put it out.  It was (I THOUGHT) supposed to be dry all weekend, I’d just finish up then.

So I get up this morning and this is what I found:

With no obvious sign of it stopping and melting any time today.  Maybe tomorrow, but not today.  Sigh.

Do I put down the straw over the snow layer, knowing that it’ll likely melt in the next couple days, or do I wait till it melts (which I do expect it to do) and put it down then?  All the plants do have a base layer on them, I just wanted it deeper and around the sides of some of the deeper container/beds.