What might be the cause of cold water entering into my washing machine very very slowly?

Most likely, your Filter Screens are clogged with dirt. There are screens on your houses and inside treaded nipples on your w/m where houses attach to. Turn water off, remove hoses, clean screens inside the hoses and clean screens inside the Male hot and cold nipples that come out of your washing machine.

Let us know how you did...

Milo, Good advice,Simple problems, Simple solutions, Thanks.

John