will cardboard kill snowdrops?

I inherited a weedy garden when I bought my house...
I was planning on putting cardboard down for a year or so to kill the many weeds around some small trees (grass, clover, flocks(?), dock, dandelions....) but then I remembered that the bed is also full of snowdrops, hundreds of them. If I cover the bed until mid-winter, will it kill the snowdrops? Am I going to have to pull the weeds out the hard way?

 

Maybe try spraying with glyphosate when bulbs not up.