Yes. I’m sensitive to milk when I’m not pregnant or nursing, so I’ve replaced the milk in this recipe with both non-dairy milk and water. It still works. You’re welcome, Internet. ;)u003cbr/u003eu003cbr/u003eMy favorite non-dairy milks to use in this cookie icing recipe are unsweetened cashew milk or unsweetened almond milk, which you would find in the refrigerated section of your grocery.u003cbr/u003eu003cbr/u003eThe only non-dairy milk I would not use for this recipe is coconut cream (from a can), as it would make the frosting entirely too thick.