Yes you can wash all your clothes in cold water and I do so a lot unless I need to remove a stain from the clothes then I use hot/warm water if the clothes can take the hot/warm water.
Using cold water instead of hot/warm water for washing your clothes can save energy and money since it doesn't use up the hot water which needs to be reheated again.
Clothes that bleed easily such as dark, bright colors or delicate fabrics should be washed in cold water.