Can I take calcium with cold water?

Yes. The temperature of water is not critical. What matters is the calcium type and dose. Calcium carbonate is best taken with food to aid absorption; calcium citrate can be taken with or without food. Limit single doses to about 500 mg elemental calcium for better absorption, and split larger daily totals. 

Review drug interactions (e.g., thyroid meds, some antibiotics, iron) and separate doses by several hours where advised. Hydration choice cold or room-temperature water does not change bioavailability meaningfully; consistency and timing relative to meals do. Always match supplement form to your tolerance and diet.