You are probaly filling with warm on the wash and the rinse is cold only or is set to cold You want to turn the water off to the cold hose going to the washer and unscrew it from the washer there will be a screen in the valve on back of washer use an old toothbrush to scrub the screen.
While the hose is off open valve and run the hose in to sink or bucket till it runs clear, turn water off and reattach hose to washer.
If the screen does not look plugged with iron, sand, or black shale etc You may need to replace the valve, supply Me with a model number if the screens are clean and I can look up where You can get the valve and give instructions on replacing the valve.
Ok You checked the hoses and inlet screens to my instructions.
Does Your washer say automatic temperature control on it?
or does the temp selector have an automatic and manual setting?
If it is an auto matictemp the cold fill for wash could be opening the hot and cold valve same time because the cold water from Your house is to cold.
If not any of these only thing left is the valve and I would need Your model number to help any further.
Remove power to the washer.
Remove the 2 screws in the console circled in red here>
Once screws are removed the console will slide forward and lift up exposing the cabinet top remove the clips in each corner and the plug that goes into cabinet>
After removing clips and plug, cabinet will tilt forward and slide away .
Turn off water and disconnect hoses to water valve, remove screw from back side that holds water valve to back panel, lift and slide out of holes in back panel, disconnect inlet hose and wire harness.
Reverse disassembly and test.
Here is a link to that water valve You'll need>