From experience, I've had issues with minerals clumping up (gypsum in particular) and not wanting to dissolve when added to cold water. These clumps are a pain to break up, and at times I've just given up and doughed in with them still being present. My general practice is to add everything once the water is above 100ish degrees. I've had no issues with minerals falling back out of suspension at times when the water has cooled back off.
For brewing at other places, I just pull a blender bottle worth of water from the mash/sparge volumes, nuke it in the microwave for a minute or so, add my minerals and mix to dissolve. Then I just add that to the main volume when brewing.