Shut off the water
Undo the hose from the washer. Check the hose some of them have a srceen as part of the sealing gacket. Run some water into a pail to be sure you have good flow.
Check the screen located on the inlet side of the washer's water control valve
There is a good chance it is clogged up
If it is clogged clean it.
Sometimes you have to remove the valve and disassemble it to clean this screen
Do not just remove the screen and run the washer without it. It is there to prevent crud from holding the valve open which could cause a flood.
If all the above are OK then your washer's water inlet valve probably needs replacing.
It is not opening all the way. | 
Cold water fills real slow 
