I like using coconut milk in my coffee. However, during summer, I like putting ice in my coffee. Some part of the coconut milk clumps up around the ice. This is organic unsweetened, so only coconut and a gum. Is there any method to prevent the clumps yet have it cold? Store in fridge, freezer, blend, add some additional stabilizing ingredient?
This is a common problem with coconut milk in cooler drinks, most commonly coffee. Coconut milk is approximately 25% fats (Source: https://en.wikipedia.org/wiki/Coconut_milk) which will coagulate in cooler temperatures or exposed to ice. You're essentially cooling the coconut milk fats with ice past their solidification state which is causing the lumps.
You can try using coconut creamers that are specifically designed for coffee since in my experience they do not clump with iced coffee. Or, there are other milks like almond that don't have as much fat content to solidify in cooler temperatures.
Another note, a lot of people seem to have this problem with iced coffee and coconut milk on forums and seem to swear by using a blender to blend the chunks away. Supposedly, this will keep the chunks from returning.
Example of others with the same issue: https://forum.whole30.com/topic/36315-lumpy-coffee-with-coconut-milk/