I am not sure of cold method, I know the HA synthesize methods are dry method e.g. solid state and mechnochemical, wet method e.g. precipitation, sol-gel, hydrothermal, emulsion or sonochemical, high temp/pressure, combination technique and synthesize from natural resources. I think you may refer to wet synthesize method where the process can be done at low temperature (e.g. room temp).
typical process of the wet method include adding one reagent (calcium or phosphate) ( such as calcium nitrate and sodium dihydrogen phosphate) to another in a dropwise manner under continuous stirring. Please remember to keep the molar ratio of Ca to P as 1.67 similar to HAp. you can also age this mixture at 100C for 3-4 days. Please look for wet synthesis method of HA and you will see many papers.
Good to remind that wet method has one disadvantage which is formation of CaP phases in the final product and presence of elemental impurities.
therefore this method might not be the best option to get HA crystal with high purity.